Question

Given that the graph of f(x) passes through the point (4,6) and that the slope of its tangent line at (x,f(x)) is 2x+4, what is f(3)?

Answer 1

This is a integral problem. You know that the tangent line, or the derivative, is 2x+4. This means the graph is on the form \[f(x) = x^2 + 4x+ C\] (by taking the integral). Hmm, you say, does this help? I mean, we have this unknown constant in here, right? Well, you can find out what C must be, because you know that when x = 4 f(x) must be 6. Solve the equation \[4^2+4\times4 + C = 6\]

Answer 2

Once C is identified, you have the complete function expression, that you can just evaluate at x = 3 to find the value you were looking for originally.

Answer 3

Capiche?

Answer 4

Yes! Thank you so much!

Answer 5

You're welcome :)