At what values of x does f(x) = x^3 - 2x^2 -4x+1 satisfy the mean value theorwm on [0,1]

x=1/3

Step-by-step explanation:

A function f is given as

in the interval  [0,1]

This function f being an algebraic polynomial is continuous in the interval [0,1] and also f is differntiable in the open interval (0,1)

Hence mean value theorem applies for f in the given interval

The value

Find derivative for f

Equate this to -5 to check mean value theorem

We find that 1/3 lies inside the interval (0,1)

-2 is the right

it is not that hard all u have to do is plot the graph

step-by-step explanation: