Question

Find an equation of the tangent line to the curve f(x) = (sins)^2 + 2tanx at x= pi/4. I worked through it and got y = 5x + 5/2 for my answer, but the answer key says that it is y - 5/2 = 5(x - pi/4). Why is the pi/4 in the answer? Thanks for any help!

Answer 1

you say y = 5 x + 2.5
then
if x = pi/4, y = 5 pi/4 + 2.5 You say

but what is f(x) at x = pi/4 ???
sin^2 = 1/2
2 tan = 2
so f(x) = 2.5

You better take 5 pi/4 off your answer

Answer 2

In other words you got the slope right but did not get b right in
y = m x + b

Answer 3

Ok thank you so much!

Answer 4

You are welcome.