Question

please explain this calc question!!

Answer 1

please explain step by step!! medal!

Answer 2

you want to find the line of the secant from x=-1 to x=1 first.

Answer 3

First, find f(-1) and f(1).
Then find the slope of this (secant) line (using the 2 end points).

Answer 4

can you explain how to do that...

Answer 5

you should be able to find f(1) and f(-1)

Answer 6

or you want help with this ?

Answer 7

-15 and 15

Answer 8

f(1)=-15
f(-1)=15

correct.

now, find the slope of the secant

Answer 9

using points (1,-15) and (-1,15) find the slope of the secant line. (just the slope formula)

Answer 10

-2/ 30 -1/15

Answer 11

slope is \(\large\color{slate}{\displaystyle \frac{\Delta y}{\Delta x} }\), and not the other way around.

Answer 12

oh sorry, -15

Answer 13

yes. -15 is the slope.

Answer 14

So, you need to differentiate the f(x) (in this case x^3-16x) and set the derivative equal to -15.

Answer 15

this will get you the x value(s) at which the slope is (also, just like the secant line) -15.

Answer 16

sorry I am lagging all the time.

Answer 17

Can you take the derivative of \(\large\color{slate}{\displaystyle f(x)=x^3-16x}\) ?

Answer 18

yes

Answer 19

ok, \(\large\color{slate}{\displaystyle f'(x)=?}\)

Answer 20

3x^2

Answer 21

close

Answer 22

you left something out

Answer 23

what is the derivative of -16x ?

Answer 24

3x^2-16

Answer 25

yup \(\large\color{slate}{\displaystyle f'(x)=3x^2-16}\)

Answer 26

you want to find the x value at which the slope is -15, so set f'(x)=-15.

\(\large\color{slate}{\displaystyle f'(x)=3x^2-16}\)

\(\large\color{slate}{\displaystyle -15=3x^2-16}\)

Answer 27

Now, solve for x.

Answer 28

x=2/3?

Answer 29

not really... i don't think so.


steps:

1. add 16 to both sides
2. divide both sides by 3
3. take the square root of both sides.

Answer 30

oh! oops sorry it is .577

Answer 31

give me exact value (if that matters for your question)

Answer 32

0.577350269

Answer 33

\(\large\color{slate}{\displaystyle -15=3x^2-16}\)

\(\large\color{slate}{\displaystyle 1=3x^2}\)

\(\large\color{slate}{\displaystyle \frac{1}{3}=x^2}\)

\(\large\color{slate}{\displaystyle \sqrt{\frac{1}{3}}=x}\)


\(\large\color{slate}{\displaystyle \frac{\sqrt{1}}{\sqrt{3}}=x}\)

\(\large\color{slate}{\displaystyle \frac{1}{\sqrt{3}}=x}\)

Answer 34

or to rationalize the denom. \(\large\color{slate}{\displaystyle \frac{\sqrt{3}}{3}=x}\)

Answer 35

okk

Answer 36

and now what?

Answer 37

@SolomonZelman ??

Answer 38

you are done, you found this x value that has the same slope as the slope of the secant

Answer 39

so the mean value theorem does apply and x is sqrt3/3??

Answer 40

yupp

Answer 41

theres only one x coordinate?

Answer 42

yes

Answer 43

(based on what we've done, for the least part... (lol))

Answer 44

thanks!(: