Question

What is

f′′(π/4), where f(x)=sinx+cosx? Show all your work. Write your final answer in simplest radical form.


If limit notation is needed in your response, use the following example as a guide:

lim

x→1 (x^2+2) should be written as lim x→1(x^2+2).

Answer 1

Refer to the photo taken.

Answer 2

`f(x)=sin(x)+cos(x)\implies \cfrac{df}{dx}=cos(x)-sin(x) \\\\\\ \left. \cfrac{d^2f}{dx^2}=-sin(x)-cos(x) \right|_{x=(\pi )/(4)}\implies -\cfrac{1}{√(2)}-\cfrac{1}{√(2)}\implies -\cfrac{2}{√(2)}\implies -√(2)`