# Max/min/critical point values

(See attached file for full problem description)

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1) Let F(x) = 2√X - X

A. Find the local maximum and minimum values of F (x) in the interval [0,9]

B. Determine whether F(x) satisfies al the conditions of MVT in the interval [0,9]. If f(x) satisfies the condition of MVT determine the 'c' value that satisfies the conclusion of the MVT otherwise state why f(x) does not satisfy the condition of mean value theorem.

C. Find the critical points of F(x)

D. Find the intervals of increase and decrease of f(x)

E. Find the inflection points of f(x)

F. Find the intervals in which f(x) is concave up and f(x) is concave down.

G. Find the local maximum and minimum values of f(x)

H. Sketch the graph of F(x)

2)

Find the vertical, horizontal, and slant asymptotes of the following functions (if they exist).

A. F(x)= (x^2 - 2 ) / (x^2 -4)

B. F(x)= (2x^2 + x + 1) / (x +1)

C. F(x)= (√x^4 -√1) - x^2

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https://brainmass.com/math/optimization/max-min-critical-point-values-54503

#### Solution Preview

Please see the attached file.

1) Let F(x) = 2√X - X

A. Find the local maximum and minimum values of f (x) in the interval [0,9]

f'(x) = 1/√x - 1 = 0

Therefore, x = 1

Clearly the local maximum exists at x = 1. The local minimum I sat x = 0.

B. Determine whether F(x) satisfies al the conditions of MVT in the interval [0,9]. If f(x) satisfies the condition of MVT determine the 'c' value that satisfies the conclusion of the MVT otherwise state why f(x) does not satisfy the condition of mean value theorem.

MVT says ...

#### Solution Summary

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