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The function $f(x)=(x^4-42x^2-80x+32)^3$ is: |
Monotonically increasing in (-4, -1) ∪ (5, ∞) Monotonically increasing in (-∞, 4) ( 1, 5) Monotonically increasing in (–4, 5) None of these |
Monotonically increasing in (-4, -1) ∪ (5, ∞) |
$f(x)=(x^4-42x^2-80x+32)^3$ $f'(x)=3(x^4-42x^2-80x+32)^2(4x^3-84x-80)$ $f'(x)>0$ $⇒4(x^3-21x-20)>0⇒4(x+1)(x+4)(x-5)>0$
$⇒x∈(-4,-1)∪(5,∞)$ So f (x) is monotonically increasing in $x∈(-4,-1)∪(5,∞)$ |
