Question

Let f be the function defined by f(x)= 5cos(pix) - e^(x^2 -4). If g(x)= inverse of f(x), find the equation of the line tangent to the graph if g at point where g(x)=2

I would just like to check that I understood how to do this properly...
derivative of f(x) = -5pisin(pix) -2xe^(x^2 -4)
Plug in 2 for x -> -4
slopes of inverse functions are reciprocals so slope at g(x)=2 would be -1/4
Then plugging in 2 for x into f(x) because g(x)=2 means f(2)=x
So gets point (4,2) in terms of g

So I get y= -1/4 (x-4) +2 as the tangent line? :3

Answer 1

@whpalmer4 @sourwing @Luigi0210 @johnweldon1993 help check? :3

Answer 2

@agent0smith @campbell_st @RadEn could you pwease help me check? :3

Answer 3

@zepdrix @robtobey @sourwing

Answer 4

hmmm?
I got f'(x)
then said slopes of inverse functions are reciprocals

Answer 5

I know that f^-1(x) doesnt equal f'(x)

I got f'(x) cuz g'(x) = 1/f'(g(x))

Answer 6

you're basically calculating 1/f'(2)

Answer 7

yes, found f'(x) plugged in x=2
then reciprocal

Answer 8

don't have to do anything by hand, calculator question

Answer 9

You did it right

Answer 10

ok thank you! :D <3

Answer 11

except one minor mistake. it's at (-4,2). not at (4,2)

Answer 12

y= -1/4 (x+4) +2 is the correct answer

Answer 13

why would it be -4 ?
http://www.wolframalpha.com/input/?i=5cos%28pix%29+-+e%5E%28x%5E2+-4%29+for+x%3D2

Answer 14

because (2,-4) is the point on f, then this means (-4,2) is the point on g(x)

Answer 15

but wolfram told me that point on f(2) = 4 ;-;
http://www.wolframalpha.com/input/?i=5cos%28pix%29+-+e%5E%28x%5E2+-4%29+for+x%3D2

Answer 16

ahh I see what's up now. I took your word for it. You said in the question that you got -4 when x = 2

Answer 17

for derivative :P
f'(2) = -4

Answer 18

f(2) = 4 xD

Answer 19

O.O ah crap. I should have read the question carefully :D.

Answer 20

so (4,2) is on g. and 1/f'(f^-1(x)) = 1/f'(2) = 1/-4 = -1/4

yeah it's correct :DD

Answer 21

Thank you ^_^

Answer 22

good job. You understand the concept ^.^b

Answer 23

I hope I do :P
APs are in two weeks >.> O_O

Answer 24

ah wait O.O

Answer 25

wut now? o.o
stop scaring me ;-; xD

Answer 26

Shouldn't we be calculating 1/f'(4) instead?

Answer 27

oh no nmv XD

Answer 28

;-; meanie why you scare my like dat >,<

Answer 29

nvm XD. This whole derivative of inverse thing can really drive you crazy XDD

Answer 30

lol ikr xD
for some reason none of the APCalcBC people know it
but apparently the APCalcAB kids are >.>

Answer 31

my grammer just failed me xD

Answer 32

Grammar errors are acceptable in a math class :D

Answer 33

:D yrsh xD