Question

Find the linearization l(x) of the function at a. F(x)=sinx a=pi/6

Answer 1

if we have a slope and a point, could we make a line equation with them?

Answer 2

It doesn't give me a point or slope just that

Answer 3

oh it s gives it to you ...

Answer 4

the point is a,f(a) and the slope is defined as f'(a)

Answer 5

y - f(a) = m(x-a)

y - f(a) = f'(a) (x-a)

Answer 6

So would I take the derivative of sin then plug in pi/6 which is1/2

Answer 7

yes

Answer 8

So my answer would just be f'(x)=cos x=cos1/2

Answer 9

y = mx - ma + f(a)

a = pi/6
f(a) = sin(pi/6)
m=f'(a) = cos(pi/6)

y = cos(pi/6)x -pi/6 cos(pi/6) + sin(pi/6)

simplify as wanted

Answer 10

Oh ok I see it now I'm overthinking this thank you

Answer 11

good luck :)