Question

Find the equation of the tangent line to
f(x)=x^2+4 at x=5

Answer 1

Have you considered a 1st Derivative?

Answer 2

ok I got 10 to

Answer 3

"10" is NOT your answer. Please read the problem statement and please don't do other peoples' homework for them.

Answer 4

Where did I go wrong derivatives are a little confusing to me so cn you help me throught this.

Answer 5

You have the slope of the tangent line at x = 5. Now, you need the equation of the tangent line. What information are you missing and how can you find it?

Answer 6

Don;t I have to find the slope

Answer 7

oh no sorry I have the slope so then don't I have to find the b in the slope equation

Answer 8

what would my y be in the y=mx+b equation

Answer 9

@farmergirl411 Very good. That is the slope-intercept form. Sadly, we have no way of finding the y-intercept. Do you know the point-slope form?

@mathematician1 The problem statement calls for the EQUATION. You stopped at the SLOPE. This is NOT a correct response.

Answer 10

How do I do the point slope form?

Answer 11

We need a point. The problem statememt gives us one. We have x = 5, the we get f(5) = 5^2 + 4 = 29 and we have a point, (5,29).

Do you see that?

Answer 12

yes

Answer 13

Perfect. All that is left is to substitute into the point-slope form of a line.

(y-29) = 10(x-5)

That is all there is to it. Of course, someone may wish that you first out it into Slope-Intercept form. Just solve for y and that will be done.

Answer 14

so the would the equation be y=10-21

Answer 15

sorry y=10x-21?

Answer 16

Awesome! Any part of that seem confusing, still?

Answer 17

no but I am just curios where did the 10 come from in the part that you posted and then you said to solve for x.

Answer 18

f'(x) evaluated at x = 5

This gives the slope of the tangent line at the given point.
This also gives the slope of the line in the point-slope form.

The two 10s are one in the same.

Answer 19

ok thanks for the explanation and your help.