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Functions and calculus

(See attached file for full problem description)

1) Consider the following function:
a) f (x) = 9x2 - x3

b) f (x) = x + 1
x - 2

c) f (x) = x2/3 (x - 5)

for each of the above functions complete the following table. Show the work to justify your answers below the table.

f(x) is increasing on
f(x) is decreasing on
Rmax of f(x) is at
Rmin of f(x) is at
x-intercept of f(x) is at
y-intercept of f(x) is at
f(x) is C. U. on
f(x) is C. D. on
P. I. of f(x) is at

2) Let f(x) = x + sin 2x on [0, 2 pie] find two numbers (c ) that satisfy the conclusion of the Mean Value Theorem. ( note there are four such numbers)


Solution Summary

This shows how to determine max, min, intercepts, concavity, and increasing/decreasing for functions.