Question

@jim_thompson5910

Alright let's finish this Part 1

We left off on 89

Answer 1

http://cyh.leeschools.net/UserContent/Documents/AP%20CalcBC%20SumAssign%2014-15.pdf

Answer 2

yeah that sounds right

Answer 3

so tell me what you have for 89

Answer 4

What I have is nada

Answer 5

Zilch

Answer 6

g(x) = x*f(x)

that's given

Answer 7

we want to find the tangent off g(x)

so we need g ' (x) to get the slope of the tangent line

Answer 8

Yis

Answer 9

when you derive x*f(x), you have to use the product rule

Answer 10

so go ahead and do that for me and tell me what you get

Answer 11

Okay

Answer 12

\[g'(x) = f(x)+x*f'(x)\]

Answer 13

good

Answer 14

now evaluate g ' (2)

this yields the slope of the tangent line at x = 2 (on g(x))

Answer 15

g'(2)=-7

Answer 16

good

Answer 17

now you need g(2)

Answer 18

this is so you know the point (x,y) that lies on g(x) when x = 2

Answer 19

y-6=-7(x-2) so D

Answer 20

correct

Answer 21

Hm no idea about 90

Answer 22

f has a positive first derivative

Answer 23

what does that mean?

Answer 24

The slope is always positive

Answer 25

what else

Answer 26

It's above the x axis?

Answer 27

f ', yes

Answer 28

what about increasing or decreasing?

Answer 29

It's always increasing

Answer 30

correct

Answer 31

so which choices can you eliminate based on this fact alone?

Answer 32

C, D and E

Answer 33

yep

Answer 34

then we move onto the fact that f '' (x) < 0 for all x

ie a negative second derivative

Answer 35

do you remember how the slopes of the secant lines correspond to concavity?

Answer 36

I don't even think we talked about secant lines

Answer 37

Or I just don't remember.

Answer 38

here's some concave up curve

Answer 39

Yes

Answer 40

and some points that lie on it