Find Maximum Value of f(x)+x | Derivative Question

  • Thread starter Thread starter Clu2.0
  • Start date Start date
  • Tags Tags
    Derivative
Clu2.0
Messages
6
Reaction score
0
1. f(x)=-x2+4x-5 (parabola)

What's the maximum value of "f(x)+x"?


sorry for my english :)
 
Physics news on Phys.org
Clu2.0 said:
1. f(x)=-x2+4x-5 (parabola)

What's the maximum value of "f(x)+x"?


sorry for my english :)
Since f(x)= -x2+ 4x- 5, f(x)+ x= -x2+ 5x- 5. That can be written as -(x2- 5x- 5. Now complete the square to dotermine where the vertex is.
 
thanks ok find the answer ("1") but in the test answer is 5/4 and teachers says it's correct
 
Isn't this just a simple case of taking the first derivative with respect to x and setting it equal to zero? This then tells you the value of x where the maximum value occurs. Then substituting this value into the function f(x)+x will tell you the maximum value at that point. This procedure does give the correct answer of 5/4.
 
thanks a lot, my carelessness
 
Or via completing the square.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Find g(x)/h(y) for a given F(x,y)
Replies
3
Views
1K
Finding the Maximum Value of f(x)=x(1-x)^n in [0,1]: A Calculus Problem
Replies
3
Views
2K
Lagrange multipliers understanding
Replies
8
Views
2K
Determining domain for C^1 function
Replies
4
Views
1K
How Do You Simplify and Analyze Taylor Polynomials for Higher Degree Functions?
Replies
5
Views
1K
Find the constrained maxima and minima of ##f(x,y,z)=x+y^2+2z##
Replies
2
Views
1K
Find f(x,y) given partial derivative and initial condition
Replies
6
Views
2K
Derivative Problem: f’(1), f’(2), f’(3), and f’(5)
Replies
11
Views
2K
What Are Local Minimum and Maximum Points in Continuous Functions?
Replies
30
Views
3K
Finding x/y-intercepts, asymptotes, derivatives, and max min
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top