Find an equation of the tangent line to the curve y=6^x
at the point (1,6)
Tangent line : y = ?

working on this a while please help!

Question

Find an equation of the tangent line to the curve   y=6^x
at the point (1,6)
Tangent line : y = ?

working on this a while please help!

zepdrix · Answer

The equation of the line tangent to the curve, $\large y=6^x$, at the point $\large x=1$ will be of the form $\large y=mx+b$ in slope-intercept form.

Err actually, let's put it in point-slope form, that will a little bit less work. :)
$$\large y-y_o=m(x-x_o)$$

Where $\large (x_o,y_o)$ is some point on the line. In this case our point is $\large (1,6)$.

$$\large y-6=m(x-1)$$

The only thing we really have to do is ~ find m.
$\large m=f'(1)$.

m is the slope of the tangent line at the point $\large x=1$

zepdrix · Answer

So all we need to do is, take the derivative of our function, then plug $\large x=1$ into it! Do you know how to take the derivative of an exponential function?

anonymous · Answer

got it thank you :)

zepdrix · Answer

cool c: