For the function f defined below, determine if f is increasing or decreasing at

Question

For the function f defined below, determine if f is increasing or decreasing at x = 2 and determine the concavity at x = 2.

f(x) = x-1 - x2

Increasing and Concave Up

Increasing and Concave Down

Decreasing and Concave Up

Decreasing and Concave Down

Suppose that the function f has the following characteristics:

then

f has a local minimum at x = 1.

f has a local maximum at x = 1.

f has neither a local maximum or a local minimum at x = 1.

there is not enough information to determine if x = 1 is a maximum or minimum.

Increasing and Concave Up

Increasing and Concave Down

Decreasing and Concave Up

Decreasing and Concave Down

Explanation / Answer

1) f'x = -1/x^2 +2x

f'' x = 2/x^3 +2

so at x =2

f'x = 4-1/4 >0 so increasing

f" x = 2/8 +2 >0

so concave up

correct option a.

2)

f'x is increasing at x=1

so f"x>0

so at x=1

fx has local minimum.

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