Let $f\left(x\right)$ = $\left\{\begin{array}{cc}ax+b& \text{,}x<2\\ x^2& \text{,}x\ge 2\end{array}\right\}$. For which values of $a$ and $b$ is $f\left(x\right)$ continuous everywhere?

Let the function be defined by $f\left(x\right)=x^3-3x^2+2$. At what value(s) of $x$ does $f\left(x\right)$ have a relative maximum?

A tangent line approximation of a function value is an underestimate when the function is:

Given the function $f(x,y)=x^2-y^2$, which of the following statements correctly describes its local maxima, local minima, and saddle points?

Which of the following statements is true about the absolute maximum and minimum values of a continuous function $f\left(x\right)$ on a closed interval $[a,b]$?

Which of the following best explains why the function $f\left(x\right)=\frac{1}{x-2}$ is discontinuous at $a=2$?

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.