Question

Help? I'm suppose to find the slope of the curve of a point of an inverse.

Answer 1

Ok. Go on...

Answer 2

If f(x) = 2x^2 + 3x + 1, let g(x) = f^-1 (x). Find the slope of the curve g(x) = f^ –1(x) at the point (6, 1).

Answer 3

First, take the derivative.

Answer 4

4x + 3

Answer 5

Now find the slope at the point (6, 1)

Answer 6

wouldn't I substitute 6 in for x?

Answer 7

Yes

Answer 8

so it would be 27?

Answer 9

Yes

Answer 10

okay now what?

Answer 11

Now the slope of the inverse function will be the reciprocal of the slope of the original function (since to get the inverse, you reflect the function over the line y=x)

Answer 12

1/27?

Answer 13

Yes. You can see here for a quick explanation why they're reciprocals http://answers.yahoo.com/question/index?qid=20120306133453AAYxtNI

Answer 14

http://webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_inverse_functions.html

I like the proof at the bottom of that page

Answer 15

okay so the answer would be 1/27?

Answer 16

HI :DD

Answer 17

lol read more carefully kayla ;)

Answer 18

https://www.hookedonphonics.com/

Answer 19

g'x is actually 1/f'(f(x))..so answer would be 1/(4.1+3)=1/7

Answer 20

@srijit see the bottom of the link below.

http://webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_inverse_functions.html

Answer 21

http://www.ccsdk12.org/mclemens/courses/APcalcAssign/MD-6A.pdf

Actually I might've worked this out wrongly. The slope is reciprocal at reflected points, but we used the original point (6,1), not the reflected point.

Answer 22

^use the very last page of http://www.ccsdk12.org/mclemens/courses/APcalcAssign/MD-6A.pdf

To find g'(6):
Find x for y=6, using f(x)= 2x^2 + 3x + 1
so x=1 and x=-5/2, but visually looking at a graph of f(x), the point for the inverse will be x=1 (tough to explain this part w/o showing using the inverse)
find the slope of f'(1) = 4(1) + 3 = 7
Then the reciprocal is 1/7.

Answer 23

sorry my typo mistake .g'x=1/f'(g(x)).g(6)=1

Answer 24

Yeah, that's probably faster, but in this case it's not quite as simple as you make it seem, since it's a quadratic function.

Answer 25

Since g(6) = 1 and g(6) = -5/2

Answer 26

its mentioned in the question only to find the slope @ (6,1) :D

Answer 27

I know. That's not the point I was making.

Answer 28

and yeah truly g(x) does not exist as f(x) is non-invertible

Answer 29

Yeah, it's an awkward question given that. I mean yeah they tell you the point (6, 1), but still.

Answer 30

i got your point :)