91Ó°ÊÓ

Find the absolute maximum and minimum values of \(f\) on the given closed interval, and state where those values occur. $$f(x)=2 x^{3}-3 x^{2}-12 x ;[-2,3]$$

Find the absolute maximum and minimum values of \(f\) on the given closed interval, and state where those values occur. $$f(x)=\frac{3 x}{\sqrt{4 x^{2}+1}} ;[-1,1]$$

Use a graphing utility to determine how many solutions the equation has, and then use Newton's Method to approximate the solution that satisfics the stated condition. $$x^{4}+x-3=0: x<0$$

Find the dimensions of the rectangle with maximum area that can be inscribed in a circle of radius 10

Find the absolute maximum and minimum values of \(f\) on the given closed interval, and state where those values occur. $$f(x)=\left(x^{2}+x\right)^{2 / 3} ;[-2,3]$$

Let \(s(t)=\sin (\pi t / 4)\) be the position function of a particle moving along a coordinate line. where \(s\) is in meters and \(t\) is in seconds. (a) Make a table showing the position. velocity, and acceleration to two decimal places at times \(t=1,2,3,4\) and 5 (b) At each of the times in part (a). determine whether the particle is stopped: if it is not. state its direction of motion. (c) At each of the times in part (a), determine whether the particle is speeding up, slowing down. or neither.

Use a graphing utility to determine how many solutions the equation has, and then use Newton's Method to approximate the solution that satisfics the stated condition. $$x^{5}-5 x^{3}-2=0 ; x>0$$

Find the absolute maximum and minimum values of \(f\) on the given closed interval, and state where those values occur. $$f(x)=x-\tan x ;[-\pi / 4, \pi / 4]$$

Verify that the hypotheses of the Mean-Value Theorem are satisfied on the given interval, and find all values of \(c\) in that interval that satisfy the conclusion of the theorem. $$f(x)=x^{2}+x ;[-4,6]$$

Use a graphing utility to determine how many solutions the equation has, and then use Newton's Method to approximate the solution that satisfics the stated condition. $$2 \sin x=x ; x>0$$