Question

The graphs of the function F (left, in blue) and G (right, in red) are below. Let P(x)=F(x)G(x) and Q(x)=F(x)/G(x). Answer the following questions.
P'(1), Q'(1), P'(6), Q'(6)

Answer 1

the graphs:
http://roy.math.umn.edu/webwork2_course_files/umtymp-calculus1-f13/tmp/gif/muzzammil-Q-raza-617-setDerivative_Rulesprob22image1.png

http://roy.math.umn.edu/webwork2_course_files/umtymp-calculus1-f13/tmp/gif/muzzammil-Q-raza-617-setDerivative_Rulesprob22image2.png

Answer 2

the first if F and the second is G

Answer 3

@dumbcow @wio

Answer 4

@zepdrix

Answer 5

@ash2326 @hartnn @Itsjustlaciee @thomaster

Answer 6

Use product rule and quotient rule to compute \(P'(x)\) and \(Q'(x)\). To evaluate this at x=1,6 you need to read of F'(1),F'(6),G'(1),G'(6) from the given graph

Answer 7

how do i find F'(1) and etc with only the graphs

Answer 8

what F'(1) means geometrically?

Answer 9

not sure

Answer 10

is there any connection between derivative and tangent line?

Answer 11

derivative is slope of tangent line

Answer 12

correct and lucky for you the graphs of F,G at points x=1, x=6 are straight lines so derivative is simply the slope of the line

Answer 13

ok. so i find the slope at those points and then do what

Answer 14

but is it a straight line for F

Answer 15

input those values into the product rule/quotient rule for F'(x), G'(x)

Answer 16

oh right F(1) is vertex of parabola, well imagine drawing a tangent line through that point....what is its slope?

Answer 17

0

Answer 18

yep

Answer 19

ok but how do i find F'(x) and G'(x)

Answer 20

i dont know their equations

Answer 21

F'(x), G'(x) are just the slopes

so we found slope at F(1) is 0 right...so F'(1) = 0

Answer 22

ok and G'(1)=3

Answer 23

no look at slope of the line again

Answer 24

rise/run=3/1

Answer 25

are you looking at line to right? when x=6 the line has slope of 3
G'(6) = 3

Answer 26

oh sorry yeah its 1. i am doing both parts at the same time

Answer 27

ok then i get F'(6) = 1/4

Answer 28

ok

Answer 29

would G'(1)=1?

Answer 30

yes you had it right

Answer 31

ok thanks. i know how to get it now

Answer 32

never mind i did something wrong

Answer 33

F'(1)=0 F(1)=1
G'(1)=1 G(1)=2
F'(6)=1/4 F(6)=3
G'(6)=3 G(6)=3

Answer 34

@dumbcow

Answer 35

this is what i got
P'(1)=1
Q'(1)=1/4
P'(6)=39/4)
Q'(6)=13/12