Question

The graphs of the function f (given in blue) and g (given in red) are plotted above. Suppose that
u(x)=f(x)g(x) and v(x)=f(x)/g(x). Find each of the following:

u'(1)=

v'(1)=

Answer 1

ho ho ho have fun
actually this is not that hard, lets do one

Answer 2

you pick it

Answer 3

number one is 1. however, I can't figure #2

Answer 4

idea is this
\(f'(1)\) is the slope of the line at \(x=1\)
it looks like \(f(1)=2\) right?

Answer 5

yea

Answer 6

and \(g'(1)=-\frac{3}{2}\) if i am reading the graph correctly
also \(f(1)=g(1)=2\) for sure

Answer 7

so \((\frac{f}{g})'=\frac{gf'-fg'}{t^2}\) replace \(f\) and \(g\) by \(2\), \(f'\) by 1 and \(g'\) by \(-\frac{3}{2}\) and do the annoying arithmetic

Answer 8

typo there, of course it should be
\[(\frac{f}{g})'=\frac{gf'-fg'}{g^2}\]

Answer 9

I got -3/2

Answer 10

i cant do that arithmetic, but i assume you are correct

Answer 11

its wrong :/

Answer 12

actually maybe not
\(g'(1)=-\frac{3}{2}\)

Answer 13

2*1-2*(-3/2)/2^2 right?

Answer 14

\[\frac{2\times 1+\frac{3}{2}\times 2}{2^2}\]

Answer 15

5/2

Answer 16

\[\frac{2+3}{4}=\frac{5}{4}\] is what i get

Answer 17

nope, thats wrong.

Answer 18

damn arithmetic is a killer

Answer 19

:/