Question

Given f(x)=3x^2+2x-1 , answer the following questions:

1.What is the EQUATION of the line that is tangent to the graph at ?
2.At what point (x, y) on the graph is its slope of 4?

Answer 1

Do you know how to take the derivative?

Answer 2

yes, I do

Answer 3

Actually, I did first question.

Answer 4

But I do not know how to do the second one.

Answer 5

Gimme a sec, I'll brb and explain it to you.

Answer 6

So you want to take the derivative as you normally do. What does that give you?

Answer 7

I just want to make sure you got the right answer for part one, because you need it for the second part

Answer 8

f'(X)= 6x+2

Answer 9

Yep, and that equation gives you the slope at any given x on the original line. Does that give you any idea on how to find the coordinates when the slope is 4?

Answer 10

set f'(x) to zero ??????

Answer 11

and solve for x???

Answer 12

That's only if you want to find the max or min of the line. Maxes and mins have a slope of 0. So this time what would you need to do?

Answer 13

find f'(4)????

Answer 14

No, that would be setting x equal to 4. Give it some thought, When you find maxes and mins, you solve for x by setting the derivative=0. What do you want to do instead this time?

Answer 15

substitute x with 4????

Answer 16

I do not know:-(

Answer 17

Don't just make guesses, make comparisons. When you solved for maxes and mins, what did you do?

Answer 18

solve for x by setting the derivative=0

Answer 19

Yes, and what is the slope of the line at the max or min?

Answer 20

0

Answer 21

So this time what slope are we concerned with?

Answer 22

4

Answer 23

Now you tell me what needs to be done. You have all the information in front of you.

Answer 24

This is not a trick question, just put two and two together

Answer 25

(1/3;4)???????

Answer 26

is it correct?

Answer 27

Okay it looks like you got the first half right. But after you set the derivative=4 and solve for x, we want to find the position on the original line where that slope of 4 is. You want to plug x back into the original and solve for y.

Answer 28

should be (1/3; 0)

Answer 29

Right???

Answer 30

What did you get for x when you set the derivative=4?

Answer 31

1/3

Answer 32

Oh nvm I made the mistake. Yes it is (1/3, 0). See, it wasn't that tough right? Just gotta make the connections

Answer 33

it was easy after you gave me a hint.
I really appreciate your help.
Thank you again.

Answer 34

Yep, glad you understand a little bit more about derivatives now (hopefully)

Answer 35

yep, it is more clearly now.