Find the equation of the line tangent to the graph of f at the indicated value of x.
-f(x) = 9 ln x; x = 1

A) y = 9x + 9
B) y = 9x
C) y = 9x - 9
D) y = 9x - 1

Question

Find the equation of the line tangent to the graph of f at the indicated value of x.
-f(x) = 9 ln x; x = 1

A) y = 9x + 9
B) y = 9x
C) y = 9x - 9
D)  y = 9x - 1

Quizplus · Accepted Answer

The derivative of f(x) = 9 ln x is f'(x) = 9/x. At x = 1, f'(1) = 9. The point on the graph is (1, 0) since f(1) = 9 ln(1) = 0. The equation of the tangent line is y - 0 = 9(x - 1), which simplifies to y = 9x - 9.

Find the Equation of the Line Tangent to the Graph