Find an equation of the tangent line to the curve
y=8^x
at the point (2,64)

Tangent line y=

Question

Find an equation of the tangent line to the curve
y=8^x
at the point (2,64) 

Tangent line y=

anonymous · Answer

Find the first derivative to find the slope at that point. 
y'=ln(8) * 8^x

anonymous · Answer

once you have the slope you can find the rest of the equation using y=mx+b. Use your point for y and x and solve or b

anonymous · Answer

So would I plug in 64 for y and 2 for x into the first derivative to get the slope? Which would make it 2.0794....5?

anonymous · Answer

the first derivative can also be written like this
$$dy/dt=\ln(8)8^x$$
use the x value to find the slope.

anonymous · Answer

dy/dx sorry

anonymous · Answer

the slope would be 133.08426

anonymous · Answer

alright so I got 133.084=ln(8)*8^2

I now go 64=133.084(2)+b to find b?

anonymous · Answer

you got it!

anonymous · Answer

Thank You so much. I appreciate it