Question

Let P(x) = F(x)G(x) and Q(x) = F(x)/G(x), where F and G are the functions whose graphs are shown.

http://www.webassign.net/scalcet7/3-2-050.gif

(a) Find P '(2). (b) Find Q'(7).

Answer 1

webassign?

Answer 2

yes!

Answer 3

\[(fg)'=f'g+g'f\] so we need 4 numbers do to this:
\[f(2),f'(2),g(2),g'(2)\]

Answer 4

For that one the answer is 3/2. I can't figure part b out

Answer 5

we have to read these off of the graph
\(f(2)=3\) that is easy over 2, up 3
\(f'(2)=0\) because the tangent line is horizontal there

Answer 6

p'(2)=F(2)G'(2)+F'(2)G(2)
(product rule)
so thatd be,
3*(1/2)+0(2)
P'(2)=3/2

Answer 7

\(g(2)=2\) again from the graph and \(g'(2)=\frac{2}{3}\)

Answer 8

no that is wrong \(g'(2)=\frac{1}{2}\)

Answer 9

plug in to the formula
\[(\frac{f}{g})'=\frac{gf'-fg'}{g^2}\] to get the answer

Answer 10

it is arithmetic from here on in

Answer 11

I just can't find f'(7) or g'(7)

Answer 12

oooh ok

Answer 13

Q'(7)=[G(7)F'(7)-F(7)G'(7)]/G'(7)^2
(quotient rule, if you can read all that)
so you have
1*(1/4)-5*(-2/3)/(-2/3)^2

so, 1/4-(-10/3)/(4/9)
I'm sure you know how to do the algebra from there, the answer should be 387/48 or 8.0625

Answer 14

\[g'(7)=-\frac{2}{3}\] from the picture

Answer 15

try and follow what i wrote, i did that all out for you haha

Answer 16

graph is a line, so slope is a constant
the constant is the slope of the line, which you read off from your eyeballs.
over 3, down 2, slope is \(-\frac{2}{3}\)

Answer 17

similarly \(f'(7)=\frac{1}{4}\) since the line goes over 4 units, and up 1 unit

Answer 18

is that part ok? because it is arithmetic from there on

Answer 19

use my arithmetic haha

Answer 20

The answer is either 10/12 , 55/12 , or 43/12

Answer 21

no... first answer is 3/2, second answer is 387/48

Answer 22

No it's multiple choice. it has to be one of the three

Answer 23

we have \(f(7)=5,f'(7)=\frac{1}{4}, g(7)=1, g'(7)=-\frac{2}{3}\) yes?

Answer 24

lets see
\[\frac{1\times \frac{1}{4}+5\times \frac{2}{3}}{1^2}=\frac{1}{4}+\frac{10}{3}=\frac{43}{12}\]

Answer 25

looks like we have a winner!

Answer 26

Woot Woot!!!! Thank you!