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April 26, 2015

Homework Help: Calculus

Posted by Leanna on Monday, February 7, 2011 at 10:53pm.

Let f be a twice-differentiable function such that f(2)=5 and f(5)=2. Let g be the function given by g(x)= f(f(x)).

(a) Explain why there must be a value c for 2 < c < 5 such that f'(c) = -1.

(b) Show that g' (2) = g' (5). Use this result to explain why there must be a value k for 2 < k < 5 such that g"(k)= 0.

(c) Show that if f"(x) = 0 for all x, then the graph of g does not have a point of inflection.

(d) Let h(x) = f(x) - x. Explain why there must be a value r for 2 < r < 5 such that h(r) = 0.

I know you have to use the intermediate value theorem and mean value theorem but don't know how.

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