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

First, we need to find the derivative of the given function. Using the chain rule and the fact that the derivative of e^x is e^x, we get:

f'(x) = 5e^(5x-8) * 5 = 25e^(5x-8)

Next, we can use the point-slope form of a line to find the equation of the tangent line at (64,3). The point-slope form is:

y - y1 = m(x - x1)

where m is the slope of the tangent line and (x1,y1) is a point on the line. Plugging in the values we know, we get:

y - 3 = 25e^(5(64)-8) * (x - 64)

Simplifying this equation, we get:

y = 25e^312 * x - 1597

This is the equation of the tangent line to the given function at the point (64,3). The answer choice that matches this equation is C.

​Find an Equation of the Tangent Line to the Graph