Find an equation of the tangent line to the graph of at the point .

Question

Find an equation of the tangent line to the graph of  at the point  . ​

Quizplus · Accepted Answer

To find the equation of the tangent line we need the derivative of the function at the given point. Using the power rule of differentiation, we get:

f'(x) = 2x - 2

Substituting x=5 into the derivative, we get:

f'(5) = 2(5) - 2 = 8

So the slope of the tangent line is 8. Now we use the point-slope form of the equation of a line to find the equation of the tangent line:

y - f(5) = f'(5)(x - 5)

Substituting x=5 and y=f(5), we get:

y - 1 = 8(x - 5)

Simplifying, we get:

y = 8x - 39

Therefore, the equation of the tangent line is y = 8x - 39, which corresponds to choice C.

Find an Equation of the Tangent Line to the Graph