91Ó°ÊÓ

In Exercises, find all relative extrema of the function. Use the Second- Derivative Test when applicable. $$ f(x)=x+\frac{4}{x} $$

In Exercises, use a graphing utility to graph the function. Then find all relative extrema of the function. $$ f(t)=(t-1)^{1 / 3} $$

Area All edges of a cube are expanding at a rate of 3 centimeters per second. How fast is the surface area changing when each edge is (a) 1 centimeter and (b) 10 centimeters?

In Exercises, find the second derivative of the function. $$ g(t)=-\frac{4}{(t+2)^{2}} $$

In Exercises, find \(d y / d x\) by implicit differentiation and evaluate the derivative at the given point. $$ y+x y=4 $$

In Exercises, find the critical numbers and the open intervals on which the function is increasing or decreasing. Then use a graphing utility to graph the function. $$ y=x^{3}-6 x^{2} $$

In Exercises, find all relative extrema of the function. Use the Second- Derivative Test when applicable. $$ f(x)=\sqrt{x^{2}+1} $$

In Exercises, find the second derivative of the function. $$ y=x^{2}\left(x^{2}+4 x+8\right) $$

In Exercises, use a graphing utility to graph the function. Then find all relative extrema of the function. $$ g(t)=t-\frac{1}{2 t^{2}} $$

A point is moving along the graph of \(y=x^{2}\) such that \(d x / d t\) is 2 centimeters per minute. Find \(d y / d t\) for each value of \(x\). (a) \(x=-3\) (b) \(x=0\) (c) \(x=1\) (d) \(x=3\)