Q. 4 - Calculus

Question

If f has a local minimum at x = 0 and a local maximum at x = 2, what can you say about f '(0) and f '(2)? Is there anything else you can say about f ' .

Step-by-Step Solution

Answer

If f has local maximum at $x=0$ and local minimum at $x=2$ then $f\left(0\right) , f\left(2\right)$ must be equal to zero .

Step 1. Given information .

Consider the given points $x=0$ and $x=2$ .

Step 2. Classify the statement .

To classify the given statement if a function f is continuous and differentiable at $x=0 , x=2$and have local maximum and minimum then the derivative of the function must be equal to zero that means $f\text{'}\left(0\right)=0$ and $f\text{'}\left(2\right)=0$ .