Question

Find the equation of the tangent line to the curve y=5sec(x)-10cos(x) at the point (pi/3, 5) written in the form y=mx+b, where m=? and b=?

also, please explain how to do this type of problem.

Answer 1

the equation of a line is normally of the form:

y = mx + b ; where m = slope and b = y int.

Answer 2

the derivative of a function IS the slope at any given point so:

m = f'(x); and the point itself is used to calibrate the rest

Answer 3

tangent line = f'(x0) (x -x0) + y0 ; where x0 and y0 are the components for the point being used

Answer 4

m = f'(pi/3) ; and b = -f'(pi/3)*(pi/3) + 5

Answer 5

that's what is confusing me. Either I'm getting the wrong derivative or I'm doing something else wrong. I get f '(x)= 5sec(x)tan(x)+10sin(x)

Answer 6

nvm, I was plugging it in wrong

Answer 7

its always the simple stuff that gets ya in the end ;)