# What is Mvt: Definition and 26 Discussions

The Marchetti MVT, later renamed SIAI S.50, was an Italian fighter of 1919 and the early 1920s.

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1. ### Hard MVT theorem proof Tutorial Q7

The tutorial question I am working on is, (a) Attempt We can use mean value theorem since ##(c: \mathbb{R} \rightarrow \mathbb{R}~countinity ) \implies (c: [-d, d] \rightarrow [c(-d), c(d)]~countinity)## Thus ##c: [-d, d] \rightarrow [c(-d), c(d)] ## is differentiable on ##(-d, d)##, then...
2. ### MHB 34 MVT - Application of the mean value theorem

$10 min = \dfrac{h}{6}$ So $a(t)=v'(t) =\dfrac{\dfrac{(50-30)mi}{h}}{\dfrac{h}{6}} =\dfrac{20 mi}{h}\cdot\dfrac{6}{h}=\dfrac{120 mi}{h^2}$ Hopefully 🕶
3. ### MHB Mean Value Theorem: Showing Change in a Function is Bounded

Ok Just have trouble getting this without a function..
4. ### MHB 3.2.15 mvt - Mean value theorem: graphing the secant and tangent lines

$\tiny{3.2.15}$ Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. Graph the function the secant line through the endpoints, and the tangent line at $(c,f(c))$. $f(x)=\sqrt{x} \quad [0,4]$ Are the secant line and the tangent line parallel...
5. ### MHB Maxima, minima, and the mvt application

Hi there I'm prepping for a big test tomorrow and I'm really struggling with this question:If f′′(x)≥−1, x belongs to (−15,15), and f′(1)=3, find the interval over which x is definitely increasing.I'm struggling with substitution because I just don't seem to have enough values. Is there a...
6. ### Don't understand the fundamentals of this problem using MVT

Homework Statement http://prntscr.com/daze68 What I don't understand: 1. "P be a polynomial with degree n" do these equations satisfy this description?: $$p(x) = (x^2 + x)^n$$ $$p(x) = (5x^2 + 2x)^n$$ etc. 2. "C1 is a curve defined by y=p(x)" c1 is essentially just the curve of the...
7. ### Question on intersection of tangent and chord

Homework Statement Show that The tangent at (c,ec) on the curve y=ex intersects the chord joining the points (c-1,ec-1) and (c+1,ec+1) at the left of x=c Homework Equations Legrange's mean value theorem The Attempt at a Solution f'(c)=ec Applying LMVT at c-1, c+1...
8. ### Question on Mean Value Theorem & Intermediate Value Theorem

Homework Statement for ##0<\alpha,\beta<2##, prove that ##\int_0^4f(t)dt=2[\alpha f(\alpha)+\beta f(\beta)]## Homework Equations Mean value theorem: ##f'(c)=\frac{f(b)-f(a)}{b-a}## The Attempt at a Solution I got the answer for the question but I have made an assumption but I don't know if...
9. ### Question on Mean Value Theorem

Homework Statement Let ###f## be double differentiable function such that ##|f''(x)|\le 1## for all ##x\in [0,1]##. If f(0)=f(1), then, A)##|f(x)|>1## B)##|f(x)|<1## C)##|f'(x)|>1## D)##|f'(x)|<1## Homework Equations MVT: $$f'(c)=\frac{f(b)-f(a)}{b-a}$$ The Attempt at a Solution I first tried...
10. ### Easy Steps for Extremas & Mean Value Theorem Problems in Calculus

Can anyone give me an easy way to find extremas and how to use the mean value theorem. This is the first thing in calculus where I read and reread and have no idea what to do when I get to the problems. It just doesn't make sense to me.. Any help is appreciated. Thank you. EDIT: Basically my...
11. ### If f(a)=g(a) and f'(x)>g'(x) for all x, use MVT to prove f(x)>g(x)

1. Homework Statement Give a graphical argument that if f(a)=g(a) and f'(x)>g'(x) for all x>a, then f(x)>g(x) for all x>a. Use the Mean Value Theorem to prove it. 2. Homework Equations 3. The Attempt at a Solution I have sketched a graphical argument to show that f(x)>g(x)...
12. ### If f(a)=g(a) and f'(x)>g'(x) for all x, use MVT to prove f(x)>g(x)

1. Homework Statement Give a graphical argument that if f(a)=g(a) and f'(x)>g'(x) for all x>a, then f(x)>g(x) for all x>a. Use the Mean Value Theorem to prove it. 2. Homework Equations 3. The Attempt at a Solution I have sketched a graphical argument to show that f(x)>g(x)...
13. ### (MVT) f(x)=sinx. Show that, for any given a and b, |sina-sinb|<=|b-a|

I'm so bad with the Mean Value Theorem. Can someone help me prove that, if f(x)=sinx, that, for any given a and b, |sinb-sina|<=|b-a|. Explain if you could too, please. Thanks a lot.
14. ### Applying the MVT to Show f(x)/x Goes to b When x Goes to Infinity

Excuse the typing please, as I am posting from my phone. Let f have domain [0,infty) and range in R. Suppose as x goes to infinity, f'(x) goes to a constant b. I wish to show that f(x)/x goes to b as x goes to infinity. I have tried numerous applications of the MVT to solve this and cannot...
15. ### How Does the Mean Value Theorem Apply to Function G(x)=x+e^-2x?

Homework Statement Consider the function g: [0,∞) -> R defined by G(x)=x+e-2x A. Use the mean value theorem to prove that |g(x2)-g(x1)|<|x2-x1| for all x1,x2 E [0,∞) with x1≠x2. B. Find all fixed points of g on [0,∞). Homework Equations MVT: f'(c) = f(b)-f(a)/b-a. The Attempt...
16. ### Accuracy of Fundamental thereom compared to MVT

Hello! The Mean Value thereom gives F(b)-F(a) = f(c).(b-a) Where f is F' and c is the value of x at which it's derivate is equal to the average rate of change over the interval a to b for F. The Fundamental thereom of calculus also gives F(b)-F(a) = (\frac{1}{b-a} \left \left \int...
17. ### Proving MVT: |sinx-siny| ≤ |x-y|

Homework Statement Prove for all real x and y that |sinx - siny| <= |x-y| Homework Equations It's a question from the Mean Value Theorem/Rolle's Theorem section. The Attempt at a Solution Honestly, I've tried. It looks somewhat similar to the triangle inequality (I think?), but...
18. ### Average Rate of Change Using MVT for Derivatives

Homework Statement The mass, m(t), in grams, of a tumor t weeks after it begins growing is given by m(t) = [te^t] / 80 . What is the average rate of change, in grams per week, during the fifth week of growth? a.) 2.730 b.) 3.412 c.) 6.189 d.) 6.546 e.) 11.131 Homework...
19. ### Proving MVT: Continuity and Differentiability of f and g on [0,1] and (0,1)

suppose f and g are continues on [0,1] and differentiable on (0,1) and f'(x)g(x) differs f(x)g'(x) for every x existing in (0,1) prove that there is a point c in [0,1] so g(c)=0 ?? for what purpose do i need to know that "f and g are continues on [0,1] and differentiable on (0,1)...
20. ### Mvt differentiation proof question

suppose f is a continues function on point x_0 prove that g(x)=(x-x_0)*f(x) differentiable on x_0?? calculate g'(x_0) i tried to think like this: if f(x) is continues on x_0 then lim f(x) as x->x_0 equals f(x_0) mvt says f'(c)=[f(a)-f(b)] cauchys mvt says...
21. ### Solving x<sin(x)<x w/ Mean Value Theorem

Homework Statement -x<sin(x)<x Homework Equations show the inequality using the mean value theorem. The Attempt at a Solution i try to find c but i keep getting tan(x) as the solution.
22. ### Rogawski 6.2 #60 (Function that D/N Satisfy MVT for Integrals)

Homework Statement Give an example of a function (necessarily discontinuous) that does not satisfy the conclusion of MVT for Integrals Homework Equations MVT for \int = \frac{1}{b-a}\int ^{b}_{a} f(x) dx The Attempt at a Solution So I should need one point of discontinuity on every interval...
23. ### Proving Limit of f'(x) = 0 with MVT

Homework Statement Let f be diff. on (0,infinity) If the limit of f'(x) as x->infinity and limit of f(n) as n->infinity both exist and are finite, prove limit of f'(x) as x->infinity is 0. Homework Equations Mean Value Theorem (applied below) The Attempt at a Solution Suppose a>0 and b>0...
24. ### Using the Mean Value Theorem to Prove Inequality for e^x and 1 + x

The following two questions are practice problems that I have been stuck on. Homework Statement Use the Mean Value Theorem to show that e^x > 1 + x for all x > 0 Homework Equations Mean Value Theorem: If f: [a,b] to R is continuous on [a,b] and differentiable on (a,b) then there...
25. ### Geometric interpretation of Generalized MVT

Homework Statement I am trying to see the geometric interpretation of the generalized MVT. It is not a homework problem, but would like to know how to interpret the equation Homework Equations [f(b)- f(a)]* g'(x) = [g(b)- g(a)]* f'(x) The Attempt at a Solution On...
26. ### Local Maximum of a Differentiable Function Using the Mean Value Theorem

Hello everyone, I'm stuck on a MVT question. Can someone please help me out? Its not really a homework question, I'm doing this question to enhance my understanding of various things. Q. Where a < x_0 < b, suppose that f(x) is differentiable in (a,b) and f'(x_0) = 0. Suppose also that for...