Find the equation of the tangent line to the graph of y=9^x at x=1.

Question

whpalmer4 · Answer

Are you taking calculus?

anonymous · Answer

In a general sense yes.

whpalmer4 · Answer

Okay, I ask because I'm going to propose that you take the first derivative of $y = 9^x$, and if you don't know calculus, you're going to say "huh?" :-)

jdoe0001 · Answer

hehe

anonymous · Answer

Oh yah, I know the derivative. $$y=9^xln(9)$$

whpalmer4 · Answer

I like you already :-)

The function is $y = f(x) = 9^x$ and the derivative is $y' = f'(x) = 9^x\ln(9)$ so we can evaluate the derivative at $x=1$ to find the slope of the tangent line.  Then we evaluate the function $f(1)$ to find the $(x_0,y_0)$ that we need to fit the line through.  We fit the tangent line with the point-slope equation:
$$y - y_0 = m(x-x_0)$$where $m$ is the value of $f'(1) = 9^1\ln(9)$

anonymous · Answer

so $$m \approx19.78$$ then just plug that into $$y-y_0=m(x-x_0)$$

whpalmer4 · Answer

When we do that, we get a nice tangent line...