f(x) from f'(x)

1 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Increasing - (-2, 0 )U( 0, 2 )
Since f '(x) displays the slope of f (x), whenever f '(x) is positive, is when f (x) is increasing.

Decreasing - ( -infinity, -2)U(2, infinity)
Whenever f '(x) is negative, f (x) is decreasing.
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2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
A extrema occurs whenever f '(x) = 0 or undefined therefore in this derivative,when x = 0 and around -5/4 and 5/4 occurs a possibility of an extrema. Most likely when x = -5/4 and 5/4 are definite extremas because it is where f (x) changes its slope from negative to positive or positive to negative. When x = 0, there is probably no extrema because the slope does change after but rather says positive.
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3 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Concaves up - ( - infinity, -5/4)U( 0, 5/4)
Concaves down - ( -5/4, 0)U( 5/4, infinity)
f(x) concaves up whenever f "(x) is positive and concaves down whenever f "(x) is negative. Whenever the slope of f '(x) is positive is where f (x) concaves up and whenever the slope of f '(x) is negative is where f (x) concaves down.
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4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The power function is x^5. Since f '(x) is a x^4 function because the function changes its slope 4 times, the antiderivative of x^4 is x^5 thus the function has to at least reach a 5th power.
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