Essentials Ex 6A

[Becky2012]

Okay, so at my school, we haven't done any calculus this year, and only about a week in 1/2, so our spec teacher has tried to teach us all of methods calculus in one class so we can move onto spec calculus, but I'm having trouble with a few of the questions.

9. Let f: (-pi/2, pi/2) -> R, f(x) = tanx. Find:
a. the coordinates of the points on the graph where the gradient is 4
b. the equation of the tangent at these points

So I've found f'(x) = sec^2x, but I don't understand what to do from there. Once I've found the coordinates I'm right with part b I think though.

[trinh]

,

,

a.
f'(x) is the gradient of f(x), at x=x; so solve , to find where the gradient=4




The above equation then 'splits into two equations', due to there being positive and negative roots:

or , where

Thus

Sub these values into the original to get your y coordinates;

EDIT: I just read that you didn't do much calculus; adjusted post accordingly

[Becky2012]

thanks, that makes sense now I forgot about the 1 on cos, and I was confused because in my head I was thinking that it couldn't be greater than one..