# Search results

1. ### Rolle's theorem, to show there's only one root

Homework Statement Homework Equations Rolle's Theorem: If f(a)=f(b)=0 then there is at least one a<c<b such that f'(c)=0 The Attempt at a Solution $$y=2x^3-3x^2-12x-6~\rightarrow~y'=6x^2-6x-12$$ The function: y': How do i know y' isn't 0 somewhere? if it's continuously descending, so i...
2. ### Min max: y=sin x+cos x

Homework Statement Homework Equations Minimum/Maximum occurs when the first derivative=0 The Attempt at a Solution $$y=\sin{x}+\cos{x}~\rightarrow~y'=\cos{x}-\sin{x}$$ $$y'=0:~\rightarrow~\cos{x}=\sin{x}~\rightarrow~x=\frac{\pi}{4}+n\cdot \pi$$ It's not correct
3. ### Min max: optimal quantity of medicine

Homework Statement Homework Equations Minimum/Maximum occurs when the first derivative=0 The Attempt at a Solution $$R'=2D\left( \frac{C}{2}-\frac{D}{3} \right)-\frac{1}{3}D^2$$ $$R'=0~\rightarrow~D=C$$
4. ### Minimization problem: Economics: quantity to order

Homework Statement Homework Equations Minimum/Maximum occurs when the first derivative=0 The Attempt at a Solution $$Q=\sqrt{\frac{2(K+pQ)}{h}}~\rightarrow~Q=\frac{2}{h}(KM+pM)$$ ##Q'=0~## gives no sense result
5. ### Min max: how much of the tax to absorb

Homework Statement Homework Equations Minimum/Maximum occurs when the first derivative=0 The Attempt at a Solution $$y=20,000+60x,~~P=200-Ax$$ $$N=xP-Y=200x-Ax^2-20,000-60x,~~N'=140-2Ax$$ Two variables
6. ### Min max problem

Homework Statement Homework Equations marginal revenue[/B] (R') is the additional revenue that will be generated by increasing product sales by one unit The Attempt at a Solution I don't know how to start. Q is the number of items sold at price x. y is the marginal cost, the cost of...
7. ### Min Max problem: the shortest distance for a light ray

Homework Statement Homework Equations Minimum/Maximum occurs when the first derivative=0 GM≤AM: ##~\sqrt{xy}\leq\frac{x+y}{2}## The Attempt at a Solution [/B] If the sum of squares of the distances (setup 2) in an arbitrary point is bigger than the sum of the squares of the shortest...
8. ### Min max problem: length of pipe from 2 towns to the river

Homework Statement Homework Equations Minimum/Maximum occurs when the first derivative=0 The Attempt at a Solution $$l_1^2+l_2^2=(a^2+x^2)+[b^2+(d-x)^2]=a^2+b^2+x^2+\left[ \sqrt{c^2-(b-a)^2}-x \right]^2$$ $$(l_1^2+l_2^2)'=2x+2\left[ \sqrt{c^2-(b-a)^2}-x \right](-1)$$...