Find the intervals on which each of the following functions is (a) increasing (b) decreasing.
f(x)=-2x3+3x2+12x+6
f’(x)=-6x2+6x+12
f’(x)=-6(x2-x-2)
=-6(x-2)(x+1)
Function f(x) is increasing for x ∈ [-1,2] and decreasing in x ∈ (-∞,-1) ∪ (2, ∞)
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Find the intervals on which each of the following functions is (a) increasing (b) decreasing.
f(x)=-2x3+3x2+12x+6
f’(x)=-6x2+6x+12
f’(x)=-6(x2-x-2)
=-6(x-2)(x+1)
Function f(x) is increasing for x ∈ [-1,2] and decreasing in x ∈ (-∞,-1) ∪ (2, ∞)