For what value of a is the liney=5x tangent to the curve y=e^(ax) at some point in the Oxy -plane?

Question

For what value of a is the liney=5x tangent to the curve y=e^ax at some point in the Oxy -plane?

Answer 1

The slope of the line y = 5x is 5.

set f' (x) = ae^(ax) = 5

e^(ax) = 5/a

ax = ln(5/a)

x = ln(5/a)/a

So the line passes through the point (ln(5/a)/a, 5/a), has a slope of 5 AND must cross the origin (or any other point on the line y=5x). Continue from here.