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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