5. Graphical Applications of Derivatives

Determine where the local and absolute maxima and minima occur on the given graph of $f\left(x\right)$.

Determine where the local and absolute maxima and minima occur on the given graph of $f\left(x\right)$.

{Use of Tech} Optimal boxes Imagine a lidless box with height h and a square base whose sides have length x. The box must have a volume of 125 ft³.

b. Based on your graph in part (a), estimate the value of x that produces the box with a minimum surface area.  

Locating critical points Find the critical points of the following functions. Assume a is a nonzero constant.

ƒ(x) = 3x² - 4x + 2

Locating critical points Find the critical points of the following functions. Assume a is a nonzero constant.

ƒ(x) = x³ / 3 - 9x

Locating critical points Find the critical points of the following functions. Assume a is a nonzero constant.

ƒ(x) = 3x³ + 3x² / 2 - 2x

The position function of a particle is given by $s\left(t\right)=t^3-6t^2+9t+2$. At what time $t$ is the speed of the particle minimum?

Which of the following could be a turning point for the continuous function $f\left(x\right)$?