Given that the graph of f(x) passes through the point ( 6, 9 ) and that the slope of its tangent line at (x,f(x)) is 2 x + 2, what is f( 2 )?
-
Given : f '(x) = 2x + 2
Integrate to get : f(x) = x^2 + 2x + C
Plug in (6, 9) to get : 9 = 6^2 + 2*6 + C
Therefore, C = -39
Thus, f(x) = x^2 + 2x - 39
Now you can work out f(2).
Integrate to get : f(x) = x^2 + 2x + C
Plug in (6, 9) to get : 9 = 6^2 + 2*6 + C
Therefore, C = -39
Thus, f(x) = x^2 + 2x - 39
Now you can work out f(2).