 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2011/paper-1/3/a/solution

Differentiating the hyperbolic cosine with the chain rule gives

g^{'} (x) = 3 cosh^{2} x sinh x

. For real

x

cosh x > 0

, so the only zero of the derivative is

sinh x = 0

, namely

x = 0

. Thus

x_{1} = 0, g (x_{1}) = 1.

Since

cosh x \geq 1

 New to topics? Read the docs here!