Find the equation of the line tangent to the graph of f at the indicated value of x.
-f(x) = 6 + ln x; x = 1
A) y = x - 5
B) y = x - 7
C) y = x + 7
D) y = x + 5

Question

Find the equation of the line tangent to the graph of f at the indicated value of x.
-f(x) = 6 + ln x; x = 1
A) y = x - 5
B) y = x - 7
C) y = x + 7
D)  y = x + 5

Quizplus · Accepted Answer

To find the equation of the tangent line at x=1, we need to find the derivative of f(x) first:

f'(x) = 1/x

Then, we can evaluate f'(1) to find the slope of the tangent line at x=1:

f'(1) = 1/1 = 1

So, the slope of the tangent line is 1. Now, we can use the point-slope form of the equation of a line to find the equation of the tangent line:

y - f(1) = f'(1)(x - 1)

y - (6 + ln 1) = 1(x - 1)

y - 6 = x - 1

y = x + 5

Therefore, the equation of the tangent line at x=1 is y = x + 5, which is answer choice D.

Find the Equation of the Line Tangent to the Graph