91Ó°ÊÓ

In Exencises \(1-8\), verify that the function satisfies the hypotheses of Rolle's Theorem on the given interval, and find all values of \(c\) that satisfy the conclusion of the theorem. $$ f(x)=x \sqrt{1-x^{2}} ; \quad[-1,1] $$

In Exercises \(5-38\), sketch the graph of the function using the curve- sketching guidelines on page \(348 .\) $$ f(x)=4-3 x-2 x^{3} $$

In Exencises \(1-8\), verify that the function satisfies the hypotheses of Rolle's Theorem on the given interval, and find all values of \(c\) that satisfy the conclusion of the theorem. $$ f(t)=t^{2 / 3}(6-t)^{1 / 3} ; \quad[0,6] $$

Find the dimensions of a rectangle of area \(144 \mathrm{ft}^{2}\) that has the smallest possible perimeter.

In Exercises \(5-38\), sketch the graph of the function using the curve- sketching guidelines on page \(348 .\) $$ f(x)=x^{3}-3 x^{2}+2 $$

evaluate the limit using l'Hôpital's Rule if appropriate. $$ \lim _{x \rightarrow 1} \frac{\ln x}{x-1} $$

Use Newton's method to find the point of intersection of the graphs to four decimal places of accuracy by solving the equation \(f(x)-g(x)=0 .\) Use the initial estimate \(x_{0}\) for the \(x\) -coordinate. f(x)=\tan x, g(x)=1-x, \quad x_{0}=1

Use Newton's method to find the point of intersection of the graphs to four decimal places of accuracy by solving the equation \(f(x)-g(x)=0 .\) Use the initial estimate \(x_{0}\) for the \(x\) -coordinate. f(x)=\frac{1}{2} \cos x, g(x)=x, \quad x_{0}=0.5

In Exercises \(5-38\), sketch the graph of the function using the curve- sketching guidelines on page \(348 .\) $$ f(x)=x^{3}-6 x^{2}+9 x+2 $$

In Exercises \(7-24\), sketch the graph of the function and find its absolute maximum and absolute minimum values, if any. $$ f(x)=2 x+3 \text { on }[-1, \infty) $$