Question

Find an equation of the line tangent to the curve given at x=a. Use a graphing utility to graph the curve and the tangent line on the same set of axes.

y=(9x)(e^x); a=-1

what is the equation for the line (y=)?

Answer 1

Know how to get the equation of the tangent line?

Answer 2

no? can you please explain the formula

Answer 3

What topic are you studying?

Answer 4

derivatives in calculus- i thinkwe'reon quotient rule

Answer 5

i know how to do formulas and stuff but i don't know how to graph

Answer 6

OK. This looks like a product rule.

Answer 7

OH, you mean you need to know how to find the point? Well the derivative gives the slope of the tangent line, right?

Answer 8

If you have slope, all you need is a point. Then you can use the point-slope formula \(y-y_1=m(x-x_1)\).

Well, they give you, "at x=a" and "a=-1" So pit -1 into the ORIGINAL formula to get the y point. Then you will have \((-1,y_1)\) to put into the point-slope formula.

Answer 9

so would it just be 9(-1)e^-1?

Answer 10

That finds the point. Then use the point and the slope of the tangent line to find the equation of the tangent line.

Answer 11

how do you find the slope?

Answer 12

The derivative.

Answer 13

@psymon

Answer 14

You said you are up to the quotient rule. Well, this would just be the product rule. Find the derivative and at that value you have the slope of the tangent line.

Answer 15

so is it 9(e^x)+(9x)(e^x)? Can you just help me out so that I'm not here all night- this thing is done in like 1 hour literally

Answer 16

*due

Answer 17

That is it. Just put -1 into that and you have the slope of the tangent line.

Answer 18

so is the answer 0?

Answer 19

The slope is 0. Which means it is a horozontal line.

Answer 20

SO WHAT'S THE EQUATION? THAT'S WHAT THE QUESTION IS ASKING. You clearly know the answer so can you just explain it to me to help me I know you're trying to help me by doing it by myself but I really don't have the time

Answer 21

As I said, it is the equation of the line at \(9(-1)e^{-1}\) with that slope. The slope is 0, so it is a horozontal line. All horozontal lines are y=k where k is a constant. So the y value from \(9(-1)e^{-1}\) is it.

Answer 22

so y=0? yes or no

Answer 23

No. y= wherver that formula gives.

Answer 24

WHAT IS THE FORMULA- JUST TELL ME

Answer 25

I did. Twice. In that post.

Answer 26

In fact, you found it earlier.

Answer 27

so y= 9(−1)e^-1? Why are you trying to disguise the answer, you clearly know what the answer is

Answer 28

I am not disguising it. I said you need to evaluate that. That is it.

Also, if you read the Code of Conduct, people can get in trouble for flat out handing out answers.

Answer 29

This should make it clearer what has happened there:
https://www.desmos.com/calculator/opudxf42nb

Answer 30

so what does evaluate it mean? Do I just solve? the answer is 0- what does y=? You're not flat out handing the answer, we've spent hours discussing this 1 problem. Flat out handing it is just posting the answer without explaining it at all.

Answer 31

Evaluate means take a number and put it in for the variable. In this case, the number given was -1.

Answer 32

that's literally exactly what i've done a bunch of times, so is y= 9(−1)e^(-1)?

Answer 33

That is it. I would simplify it (multiply the -1 so it becomes -9) but other than that, it is done. This one had no steps past that because the slope was 0. If the slope was something else, it would have taken more work.

Answer 34

thx bro

Answer 35

np. Have fun. As you go on in calc you will see more problems that yseEVERY part of math before it. If there was something in the past that confused you, I would brush up because they hit on everything.