Suppose f(x) is a differentiable function with f(-1) =2 and f(2) =-1. The differentiable function g(x) is defined by the formula g(x) = f(f(x)).  (a) Compute g(-1) and g(2). Explain why g(x) = 0 must have at least one solution between -1 and 2.  (b) Compute g'(-1) and g'(2) in terms of values of f and f'. Verify that g'(-1) =g'(2). Explain why g''(x) = 0 must have at least one solution between -1 and 2.

Suppose f(x) is a differentiable function with f(-1) =2 and f(2) =-1. The differentiable function g(x) is defined by the formula g(x) = f(f(x)). 

(a) Compute g(-1) and g(2). Explain why g(x) = 0 must have at least one solution between -1 and 2. 

(b) Compute g'(-1) and g'(2) in terms of values of f and f'. Verify that g'(-1) =g'(2). Explain why g''(x) = 0 must have at least one solution between -1 and 2.