Chapter 2.8, Problem 18E

To determine

To sketch: The graph of a function whose first and second derivative are always negative

Answer to Problem 18E

  $f\left(x\right)=-e^x$

Explanation of Solution

Given: Any function

Concept used:

Definition of derivative: $f^{\text{'}}\left(x\right)=\frac{df\left(x\right)}{dx}$

Let $f\left(x\right)=-e^x$ be any function.

See graph first on the right. First derivative is always negative means the function is always decreasing and second derivative is always positive means the function is always concave up.