Estimate f ' (pie/ 4) by using a graphing utility

[priscilla98]

Homework Statement

Let f (x) = sin x. Estimate f ' (pie/ 4) by using a graphing utility.

a) 1 / 4
b) √2 /2
c) 1 / 2
d) pie / 4

The Attempt at a Solution

Is it sin (45) = √2 /2. I'm wondering if b is the answer.

 

[Kevin_Axion]

It is, use the unit circle and it will give you that answer. But it isn't [tex]sin(45)[/tex] it says [tex]f'(\frac{\pi}{4})[/tex] and [tex]f(x)=sinx[/tex] taking the derivative of [tex]f(x) = f'(x)= cosx[/tex]. Since on the unit circle [tex]cos(45)=sin(45)[/tex] then they both equal [tex]\frac{\sqrt{2}}{2}[/tex]

[tex]\frac{d}{dx}sinx = cosx[/tex]

[tex]cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}}[/tex]