Question

The graph of y = f ′(x), the derivative of f(x), is shown below. Given f(–4) = 2, evaluate f(4).

Answer 1

@mathstudent55 @amistre64 @CausticSyndicalist @dan815 @EclipsedStar @perl @jagr2713 @TheSmartOne @texaschic101 @jdoe0001 @Nnesha @abb0t @tHe_FiZiCx99 @tanya123 @poopsiedoodle @FibonacciChick666 @vera_ewing @Abmon98 @Jaynator495 @Firejay5 @amorfide

Answer 2

Oh this should be easy!

Answer 3

Okay so given the derivative the area under the curve is the value for the normal function right?

Answer 4

right so

Answer 5

What's the area under the curve from (-4,0)

Answer 6

2

Answer 7

@alisyed5865

Answer 8

Base times height

Answer 9

divided by 2

Answer 10

4 times 2 divided by 2... Is that 2?

Answer 11

yep

Answer 12

@alisyed5865

Answer 13

So you're telling me... 4 multiplied by 2 then divided by 2 is 2?

Answer 14

no thts 4

Answer 15

opps i thought u were asking me to divide 4/2

Answer 16

my mistake...so then what do we do after having the value of 4? @alisyed5865

Answer 17

Okay okay good.

Answer 18

Now from -4 to 0. You must remember that the area of that curve is negative! So it's -4!

Answer 19

@alisyed5865 is that the final answer? because thats not an answer choice

Answer 20

Obviously not you're not close to done.... sheesh

Answer 21

Anyways moving on what's the area under the curve from 0 to 4

Answer 22

neg 4

Answer 23

No this area is above the x axis... So it's positive 4.

Answer 24

ohhh, i see now! :)

Answer 25

Okay so you have f(-4)=2 then you have \[\int\limits_{-4}^{0} f(x) = -4\] \[+\int\limits_{0}^{4} f(x)=4\]

Answer 26

So you get 0 from the integral -4 to 4. But you're not done yet you have to add the initial condition which is f(-4)=2 so the answer should be 2.

Answer 27

so a?

Answer 28

Yea

Answer 29

can u do another problem w/ me?

Answer 30

Uh sure

Answer 31

The graph of f ′(x) is continuous and increasing with an x-intercept at x = 0. Which of the following statements is false?

The graph of f is always concave up.
The graph of f has an inflection point at x = 0.
The graph of f has a relative minimum at x = 0.
The graph of the second derivative is always positive.

Answer 32

So if a graph is increasing that means it's derivative will always be positive... and if f''(x) is always positive what does that mean?

Answer 33

that that is true, statement d is so therefore letter d is out

Answer 34

And so is option A because being positive and concave up in f''(x) are the same thing.

Answer 35

@alisyed5865 Right!

Answer 36

@alisyed5865 hello??

Answer 37

Okay so now if the function is increasing always and has an x intercept at 0 that means that f'(x) goes from negative to positive there then what does that mean.

Answer 38

@alisyed5865 this means that c is another truth hence b is the false statement leftover

Answer 39

@mathstudent55 @amistre64 @CausticSyndicalist @dan815 @EclipsedStar @perl @jagr2713 @TheSmartOne @texaschic101 @jdoe0001 @Nnesha @abb0t @tHe_FiZiCx99 @tanya123 @poopsiedoodle @FibonacciChick666 @vera_ewing @Abmon98 @Jaynator495 @Firejay5 @amorfide

Answer 40

can somebody check this and make sure its right?

Answer 41

what am I checking, too many comments

Answer 42

is answer b right? @amorfide @alisyed5865 left

Answer 43

yes I believe it is correct

Answer 44

ok thank you

Answer 45

the graph is symmetric, so f(-4)=-2
f(4)=2
since


since the graph is symmetric, then these side lengths are the same, therefore it would just be the same answer different sign if that makes sense