Question

Find an equation of the tangent line to the of the function at the given point.

f(x) = 3x2 – In x (1,3)

The answer is 5x-y-2=0 but I don’t know how to get to it.

Answer 1

Explanation:

The slope of the tangent line is equal to the derivative.

f(x) = 3x² − ln x

f'(x) = 6x − 1/x

f'(1) = 6(1) − 1/1

f'(1) = 5

Use point-slope form:

y − 3 = 5 (x − 1)

Simplify:

y − 3 = 5x − 5

0 = 5x − y − 2