Find the max and min alues attained by the function

Question

Solve the following:

Problem 1-

Find the Max and Min. values attained by the function ( on the interval [0,2]

h(x)=x-1/x+1

Problem 2-

A mass of clay with a volume is formed into two cubes. What is the minimum possible total surface area of the two cubes? What is the Max?

432in^3

Problem 3-

The equation has 3 distinct real roots. Approximate their locations by evaluating f at -2,-1, 0, 1, and 2. Then use Newton's method to approximate each of the 3 roots to four-place accuracy.

f(x)x^3-3x+1

Problem 4-

Sand falling from a hopper at forms a conical sand pile whose  radius is always equal to its height. How fast is the radius increasing  when the radius is 5ft?

10πFT^3/sec

Problem 5-

Find the open intervals on the x-axis on which the function (Figure 5.1) is increasing and those on which it is decreasing.

f(x)=x^2/x-1

Problem 6-

What is the maximum possible volume of a right circular cylinder with a total surface area of Figure 6.1 (including the top and the bottom)?

600πIN2

Problem 7-

Find the interval on which the function  is  increasing and decreasing. Sketch the graph of y = f(x), and identify any  local maxima and minima. Any global extrema should also be identified.

f(x)=(x-2)2(x+3)2

Problem 8-

Find the exact coordinates of the inflection points and critical points of  the function on the interval (-10, 10)

f(x)=2x3+3x2-180x+150

Problem 9-

Graph f(x). Identify all extrema, inflection  points, intercepts, and asymptotes. Show the concave structure clearly  and note any discontinuities.

f(x)=x²/x-1