Question

Given the function `f(x) = absx`, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-4,6] and find the c?

Answer 1

Sans the node x = 0, the function is differentiable. For negative x, f'=-1 and for positive x, f'=1. So, c is infinite valued (arbitrary), as any x in an interval, sans x=0, is c... .

Explanation:

|f(x) = |x|# is the combined equation for

the pair of radial lines `y=-x`, for `x<0 and y=x`, for `x>0`.

x=0 is a node.

`f'=-1`. for `x<0 and f'=1`, for `x>0`.

Sans the node x = 0, f is differentiable. .

c in Mean Value theorem is infinite valued (arbitrary), as any x is c, in

any interval, sans x=0, ... .