Question

The graph of x-2y=9 is parallel to the normal line to the graph of f(x) when x=5. What is the value of f'(5)? Justify your answer.

Answer 1

x-2y=9 slope is 1/2 slope that belongs to the normal line is -2 not sure what else to do

Answer 2

ok I am reading this incorrectly. Maybe my slope is 1/2

Answer 3

slope of \(x-2y=9\) is \(\frac{1}{2}\) so slope of normal line is \(-2\)

Answer 4

oh i see you said that
there is nothing else to do except say \(f'(5)=-2\) that is all

Answer 5

Note: the slopes of two lines that are perpendicular are negative reciprocals, which satellite73's comment aptly illustrates.

Answer 6

You say you're in precalculus, but I see you finding the derivative: f'(x). How's that?

Answer 7

parallel to the normal line?

Answer 8

My username is precal but I tend to study calculus for fun

Answer 9

Calculus is not my strong point, I struggle with many calculus concepts. Solving 600 pages of calculus just for fun.

Answer 10

It surely adds to your problem solving skills if you understand that the derivative of a function represents the slope of the tangent line to the curve of that function at a certain point / certain x-value.

Answer 11

Let's go back to the beginning. Re-read the original question. What are you sure you are able to do correctly? What are you not so sure about?

Answer 12

The graph of x-2y=9 is parallel to the normal line.
y=(-9/2)+(1/2)x is the function and the slope is 1/2 that is parallel to the normal line of f(x). I am assuming that f(x) is some other function and not x-2y=9

Answer 13

What leads you to assume that f(x)=-9/2 + (1/2)x?

Answer 14

Let's suppose that we DON'T know f(x). What is the slope of the TANGENT line to the graph of this function at x?

Answer 15

No, I am not assuming that f(x) is that.
I solved for y to determine the slope.
I don't know anything about f(x) except that this line is parallel to the normal line

Answer 16

m=-2 this slope is the slope of the tangent line

Answer 17

because the tangent line and normal line are perpendicular

Answer 18

All right. Let's back up a bit. You are dealing with a function named f(x), right?
What is the derivative of f(x)?

Answer 19

This is some type of AP Calculus AB problem, I know I am overlooking something.

Answer 20

f'(x)

Answer 21

that's right.

Now, what is the slope of any line that is PERPENDICULAR to this tangent line? Write it symbolically.

Answer 22

-1/f'(x)

Answer 23

Yes, my point exactly.

Answer 24

Now, what is the slope of that given line?

Answer 25

1/2

Answer 26

yes, both lines are parallel and therefore have the same slope

Answer 27

Sorry, my sentence was 'way off. I'm going to delete it after re-writing my question.

Answer 28

We are told that the given line and the normal line to the curve at x=5 are parallel. What does that say ab out their slopes?

Answer 29

so is my answer -1/-2 or 1/2

Answer 30

so satellite was incorrect? Not even sure I am correct but I am following your logic

Answer 31

other slope is negative reciprocal

Answer 32

now I am not sure, is the solution -2 or 1/2

Answer 33

slope is 1/2 in the beginning

Answer 34

slope of x-2y=9 is 1/2

Answer 35

I agree that the slope of the given line is 1/2.
You correctly found an expression for the slope of the normal line. For review, type it out again here.

Now equate those two quantities and solve for f'(5).