Question

if f(8)=5 and f'(8)=12, find the best estimate for f(9).

Answer 1

8/5=9/x

I guess

Answer 2

you guess?

Answer 3

How can a function have f(8)= 5 and f(8) = 12. This is not a function then.

Answer 4

@mathstudent55 it says f prime(8)= 12

Answer 5

Oh, ok, thanks. I couldn't see that.

Answer 6

@Hero, what do you mean, how would I use it?

Answer 7

I was mainly speaking against @timo86m setup

Answer 8

ohhh

Answer 9

so, what's next?

Answer 10

ok, make me think :)

Answer 11

isn't it (8,5)?

Answer 12

ok, so you don't have to use f '(8)=12 at all?

Answer 13

oh ok, thank you!

Answer 14

would it be the same if i were to use the point slope formula, and then plug 9 into the equation I get out of it?

Answer 15

Okay, I have it for sure. Sometimes I have to talk my way through these. Basically the slope is given:

f'(x) = m

In this case:
f'(8) = 12

Therefore the slope is 12. Thus rise/run = y/x = 12/1

Now, plot the given point (8,5).
Next, move the point up 12 units, and 1 unit to the right.
The next point is (9, 17)

Answer 16

ok thank you :)

Answer 17

@hero Does a problem like this assume that f(x) is a linear function?

Answer 18

We're not assuming the function is linear. We used the definition of slope to find the next point.

Answer 19

But the slope provided was at the specific point where x = 8. Couldn't the slope also have changed between x = 8 and x = 9? If f(x) is a third degree polynomial, the slope would be quadratic, and may be different at f(9).

Answer 20

By the way, it says to estimate. So we can assume the that the next point is close to (8,5)

Answer 21

Ok, I think that's the key.

Answer 22

Thanks

Answer 23

There's no other way to figure this out

Answer 24

What you mentioned about degree of polynomial is exactly the reason why there is no other way. We are not given the formulas for f(x) or f'(x). So we have to make some assumptions in order to solve it.

Answer 25

I get it now, thanks.