Is $f (x) = (x + 3) (x - 2) (x - 2)$ $f(x)=(x+3)(x-2)(x-2)$ increasing or decreasing at $x = - 2$ $x=-2$ ?

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Is $f (x) = (x + 3) (x - 2) (x - 2)$ $f(x)=(x+3)(x-2)(x-2)$ increasing or decreasing at $x = - 2$ $x=-2$ ?

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Answer 1 · 2016-01-17T19:23:58

increasing at x = - 2

Explanation:

first expand the brackets of the function (using FOIL) then differentiate f(x) and check it's value.

(x + 3 )( $x^{2} - 4 x + 4) = x^{3} - 2 x^{2} - 8 x$ $x^2 - 4x + 4 ) = x^3 - 2x^2 - 8x$

f(x) = $x^{3} - x^{2} - 8 x + 12$ $x^3 - x^2 - 8x + 12$

$rArr f'(x) = 3x^2 - 2x - 8$

$f'(-2) = 3(-2)^2 -2(-2) -8 = 12 + 4 - 8 = 8 > 0$

since f'(-2) > 0 then f(x) is increasing at x = -2 .

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Is $f (x) = (x + 3) (x - 2) (x - 2)$ $f(x)=(x+3)(x-2)(x-2)$ increasing or decreasing at $x = - 2$ $x=-2$ ?

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