Find the values of Tangent line that isn't given

Question

I'm going through a review for an upcoming exam and this has me stumped:

The line tangent to $y=f(x)$ at $x=3$ passes through the points $(0,10)$ and $(10,30)$. Find the values of $f(3)$ and $f'(3)$.

I tried basic formatting for the functions, but the preview window showed \int as not working. f' is indicating the first derivative.

Can you find the equation of the tangent line? – David Mitra Jul 10 '13 at 16:02 — David Mitra, Jul 10 '13 at 16:02

BlackAdder · Accepted Answer · 2013-07-10T16:07:12.980

1

Equation of tangent is $y=2x+10$, so $f'(3)=2$. So $f(3)=16$.

To do this, note that the tangent line intersects the $y$-axis at 10. And a quick computation of the gradient gives you $\frac{30-10}{10-0}=2$. And you should be home from there.

edited Jul 10 '13 at 16:07

answered Jul 10 '13 at 16:02

BlackAdder

4,029

This worked great for me. I must've had a brain fart because once I saw it, it all came flooding back. – GeoffM Jul 10 '13 at 16:15
No problem, all the best for your exam. – BlackAdder Jul 10 '13 at 20:40

Find the values of Tangent line that isn't given

1 Answers1