Find a point on the graph of the function f(x)=3e2x , where the tangent line to the graph is parallel to the line y=3x-1

Question

Find a point on the graph of the function f(x)=3e^2x , where the tangent line to the graph is parallel to the line y=3x-1

Answer 1

f(x) = 3e^2x. You want to know the value of x where the tangent line to the curve f(x) is parallel to the line y = 3x - 1.

The line y = 3x - 1 is linear and so it always has the same slope, 3.

The first derivative of a function at x has a value equal to the slope of the tangent line to the function at that point. Therefore, the problem really asks for what value of x is df/dx = 3

df/dx = 6e^2x = 3

e^2x = 1/2

Take the natural logarithm of each side.

2x = ln(1/2)

2x = -ln2

x = -ln2 / 2