Question

Verify the Rolle’s theorem for the following function f(x)=x^3+5x^2-6x,x(0,1)​

Answer 1

Step-by-step explanation:

Given f(x)=x

2

+5x+6=(x+2)(x+3) on [−3,−2].

Now f(−3)=0=f(−2).

Also the given function is continuous in [−3,−2] since polynomial function is continuous every where and differentiable also. So the given function is also differentiable in (−3,−2).

So the given function satisfies all the conditions for Rolle's theorem in [−3,−2].

I hope it helps you

please mark me as a brainlist