Show that the function f(x)=1-|x|, [-1,1] does not satisfy the hypotheses of the mean value theorem on the given interval.
Also how do I graph the function together with the line through the points
A(a,f(a)) and B(b,f(b)).
Also how do I find values of c in (a,b) that satisfy f'(c)=f(b)-f(a) / b-a
Thank you so much in advance.
The function is not differentiable at 0. The assumption of the MVT is that is is continous, and differentiable on the interval.
Points a will have to be in the same side of origin as point b ie, either -1 to 0, or 0 to 1. Given that, then c will be between a and b.