Question

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

Tangent line y=

Answer 1

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

Answer 2

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

Answer 3

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?

Answer 4

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

Answer 5

dy/dx sorry

Answer 6

the slope would be 133.08426

Answer 7

alright so I got 133.084=ln(8)*8^2

I now go 64=133.084(2)+b to find b?

Answer 8

you got it!

Answer 9

Thank You so much. I appreciate it