Question

The tangent line to y=f(x) at (3,10) passes through the point (8,−1). Compute the following.

a.) f(3)=

b.) f′(3)=

Answer 1

what is f(3)? its the value of y at x=3

Answer 2

from the question, you can see that at x=3, y is 10.

Answer 3

@physo ok that makes sense

Answer 4

use the same logic to do (b)

Answer 5

i don't get how unless its the same answer

Answer 6

first derivative is the gradient of the tangent at that specific point and gradient = (y2-y1)/(x2-x1)

Answer 7

where (x1,y1) and (x2,y2) are any 2 points on the tangent line

Answer 8

slope= 11/-5

Answer 9

perfect i got it

Answer 10

good job!