Posted by **Anonymous** on Monday, April 19, 2010 at 8:18pm.

Determine the equation of the line that is tangent to y=8^x at the point on the curve where x=1/2

- calculus -
**Reiny**, Monday, April 19, 2010 at 9:34pm
first the easy part,

when x = 1/2 y = 8^(1/2) = √8

so our point is (1/2, √8)

I will take ln of both sides

ln y = ln 8^x

lny = x(ln8)

(dy/dx) / y = ln8

dy/dx = ln8(8^x)

so at (1/2, √8)

dy/dx = (ln8)(√8)

so you have m = ln8(√8) and the point (1/2, √8)

find the equation of the line.

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