Question

How do you determine all values of c that satisfy the mean value theorem on the interval [1, 1.5] for `f(x)=sinx`?

Answer 1

`c~~1.25`

Explanation:

`f'(x)=cosx`

Mean Value Theorem

`f'(c)=(f(b)-f(a))/(b-a)`

`cos c=(f(1.5)-f(1))/(1.5-1)`

`cos c=(sin(1.5)-sin(1))/(1.5-1)`

`cos c=(sin(1.5)-sin(1))/(1.5-1)`

`cos c =0.3120480036`

`c=cos^-1 0.3120480036`

`c~~1.25`