Question

The tangent line to y= f(x) at (4,-6) passes through the point (10,9) Compute the following, f(4) and f'(4)

Answer 1

well you know that the slope of the tangent line at the point (4,-6) is f'(4) ?

Answer 2

Right!

Answer 3

so we can compute f'(4) using the two points the tangent line passes through : (4,-6) ,(10,9)
can you do it ?

Answer 4

Maybe... do I just find the slope using the y-y/x-x formula and thats my answer?

Answer 5

yes it is ! (for f'(4))

Answer 6

awesome! now I'm completely lost on f(4) haha

Answer 7

well .. f(4) is right in front of your eyes! you got the point with x=4 that f passes through it!!

Answer 8

okay I'm completely confused.. I'm sorry! I'm way too new at this haha. I just do y=mx+b and plug in 4 for x, the answer to f'(4) for the slope?

Answer 9

f'(4) is the slope of the tangent line.. we know that the tangent line passes through the points : (4,-6) ,(10,9)
so .. all you have to do is calculate the slope of the line that passes through those two points and get f'(4) (just as you said up there)

Answer 10

f'(4) = (9 - (-6)) / (10 - 4) = 15 / 6 = 2.5

Answer 11

you DONT need to find the line equation y=mx+b for this question.. you just need the slope of the tangent line (f'(4))

Answer 12

Alright, I think I get it! Thanks a bunch!

Answer 13

wait.. do you know what is f(4) ?

Answer 14

it's easier than f'(4)

Answer 15

it's given in the question!

Answer 16

-6?

Answer 17

Thank you :)

Answer 18

yes.. very good :)