Question

find an equation for the tangent line to the graph of f at the point P (pi/4, f(pi/4)) when
f(x)= 6 tan(x)

Answer 1

do you know the derivative of \(6\tan(x)\) ?

Answer 2

6sec^2(x) i think

Answer 3

Do you know how to find the slope of the tangent line?

Answer 4

no the teacher is whack and lazy and is being investigated by the university math department

Answer 5

yes that is right
replace \(x\) by \(\frac{\pi}{4}\) and you are done
the derivative is the formula for the slope

Answer 6

the slope of the tangent line is the derivative

Answer 7

that does not answer what is asked

Answer 8

you must make an equation

Answer 9

right.

Answer 10

Things you need to make an equation of the tangent line

Answer 11

1. slope of the tangent line

Answer 12

2. the point which the tangent line passes through

Answer 13

To get the slope, you take the derivative and plug in your value from your point.

Answer 14

so plug in \[\frac{ \pi }{ 4 }\] into your derivative. That gives you your slope....

Answer 15

So, what's your slope?

Answer 16

12 i think

Answer 17

no?

Answer 18

You're saying \[\sec ^{2}(\frac{ \pi }{ 4 }) = 12?\]

Answer 19

where is the six

Answer 20

right. so 6sec^2(pi/2) = 12?

Answer 21

i think im not sure

Answer 22

haha you're right.

Answer 23

so. you have your slope.

Answer 24

ok sorry im slow :(

Answer 25

now your point is (pi/4, f(pi/4))

Answer 26

solve for your y in your point.

Answer 27

idk how

Answer 28

well your point is (x,y) so pi/4=x and f(pi/4)=y, they're basically telling you that your y is the answer you get when you plug pi/4 into your original function.

Answer 29

right now what

Answer 30

y=f(pi/4)=6tan(pi/4)

Answer 31

so solve 6tan(pi/4)