Find an equation of the tangent line to the graph of at the point (64,3).
A)
B)
C)
D)
E) none of the above

Question

​Find an equation of the tangent line to the graph of  at the point (64,3). ​
A) ​ 
B) ​ 
C) ​ 
D) ​ 
E) ​none of the above

Quizplus · Accepted Answer

To find the tangent line at the point (64,3), we need to take the derivative of the function and evaluate it at x=64.

11ea8970_6a04_4b26_861b_27f0d896bbf7_TB1301_11 = x^2/4 - 16/x

Using the power rule, we get:

f'(x) = x/2 + 16/x^2

Evaluating at x=64, we get:

f'(64) = 64/2 + 16/64^2 = 33/32

So the slope of the tangent line at (64,3) is 33/32.

Using the point-slope form, we can write the equation of the tangent line as:

y - 3 = (33/32)(x - 64)

Simplifying, we get:

y = (33/32)x - 1263/32

This matches choice C, so the answer is C.

​Find an Equation of the Tangent Line to the Graph