find the equation of the line tangent to y=2secx at =pi/4 , someone can plz explain me step by step??

Question

jdoe0001 · Answer

tangent to y=2secx at x=pi/4  ?

jdoe0001 · Answer

someone, no name, just deleted 2 lines :P

anonymous · Answer

oohh yes its x=pi/4

jdoe0001 · Answer

keep in mind that a derivative is the EQUATION TO FIND THE SLOPE for that function
is not the slope value itself

so   what would be the derivative of 2sec(x)?

anonymous · Answer

2secxtanx

whpalmer4 · Answer

Okay, so the slope of tangent line at $x=\frac{\pi}{4}$ is the value of the first derivative at that same value of $x$:

$$m = 2\sec (\frac{\pi}{4})\tan(\frac{\pi}{4}) =$$
Now use that in addition to the point-slope formula to establish the tangent line:
$$y-y_0 = m(x-x_0)$$You'll need to evaluate $y_0 = 2\sec(x_0)$ with $x_0 = \dfrac{\pi}{4}$ to fill in all the blanks.

whpalmer4 · Answer

If you do it correctly, you'll end up with a tangent line like the one illustrated in the attached graph.

anonymous · Answer

do i have to draw that ?

whpalmer4 · Answer

I don't know, does your problem ask you to do so?  I'm just illustrating the result.  If you made a mistake, you might end up with something like one of these two:

whpalmer4 · Answer

I'm a big fan of checking answers.  A graph is an obvious way to check the answer to a problem like this, wouldn't you say?