Question

show that f(x) = x³+6x²-36x+7 is decreasing function in the interval (-6,2)​

Answer 1

Answer:

Given, f(x)=x3−6x2−36x+2

On differentiating w.r.t. x, we get

f′(x)=3x2−12x−36

For decreasing, f′(x)<0

⇒3(x2−4x−12)<0

⇒(x−6)(x+2)<0

⇒−2<x<6

∴xϵ(−2,6).

Explanation:

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