Evaluating derivatives

Question

"If the tangent line to $y = f(x)$ at $(4,3)$ passes through the point $(0, 2)$, find $f(4) $and $f'(4)$"

I'm not sure even where to start on this. The language of this problem is very confusing to me, I don't have good English. I would think f(4) = 4 since y = f(x), but that seems too easy.

Can someone please point me in the right direction of how to even solve this? It feels so overwhelming

It's that easy. Think now in the derivative. – Martín-Blas Pérez Pinilla Feb 09 '14 at 00:04 — Martín-Blas Pérez Pinilla, Feb 09 '14 at 00:04
I think you mean $f(4)=3$, and yes, it is that easy. – Jack M Feb 09 '14 at 00:06 — Jack M, Feb 09 '14 at 00:06

score 2 · Accepted Answer · answered Feb 09 '14 at 00:08

You're given that a line is tangent to a function at $(4, 3)$. Thus, this point has to lie on the curve, and so $f(4) = 3$.

Now, consider that you have two points on the tangent line, $(4, 3)$ and $(0, 2)$. You can find the slope of the line passing through these points, and that will give you $f'(4)$.

Evaluating derivatives

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