Question

If the line tangent to the graph of the function F at the point (1,7) passes through the point (-2,-2), then F'(1)=?

Answer 1

when x=1; what does y still equal?

Answer 2

the tangent line to a function at any given point; will always have the gien point in common

Answer 3

gien means given ....

Answer 4

F'(1) measures the slope when x=1, so just find the slope of the tangent line.

Answer 5

F(x) meets F'(x) at ... x

the value at F(1) is no different for the value of F'(1) simply because (1,7) IS the point they have in common to each other. So if the value of F(1) = 7; the the value of F'(1) = .... well, its still gonna be 7.

Answer 6

Why would anyone need to find the slope of the tangent line at x=1 in order to determine the value of F'(1)?

Answer 7

If i lean against the wall, the point where my elbow and the wall meet are "tangent". The point where they meet never changes regardless of if i view it from the walls "equation" or my bodies "equation".

Answer 8

F(x) is an unknown function and F'(x) is the derivative of the function. Derivatives are slopes. When you plug in 1 into the derivative you get the slope of the line tangent to the function at x=1. But the function is unknown so you can't take the derivative, but you know two points the tangent line goes through so find the slope of the tangent line in order to get F'(1)

Answer 9

I think you're taking the tangent line as F(x) and the function as F'(x). Actually, the function is F(x) and F'(x) is the derivative of the function. The line is just a tangent line that you use.

Answer 10

(1, 7)
-(-2,-2)
------
3,9; the slope = 9/3 = 3

The equation of the tangent line is:

y = 3x -3(1)+7

y = 3x + 4

yeah, i think i see what i was doing :)

Answer 11

the slope of the tangent line; f'(1) = 3