# 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?

##### 1 Answer

Jul 12, 2016

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

x=0 is a node.

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, ... .