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

Question

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

Quizplus · Accepted Answer

To find the equation of the tangent line, we need to find the derivative of the function first:

f'(x) = 2x - 1

Then we evaluate the derivative at the given point, x = 5:

f'(5) = 2(5) - 1 = 9

This is the slope of the tangent line. We also know the point (5, 24) is on the tangent line. So we can use the point-slope form of a line to find the equation of the tangent line:

y - 24 = 9(x - 5)

Simplifying this equation, we get:

y = 9x - 21

This is the equation of the tangent line to the graph of the function at the point (5, 24). The answer is B.

Find an Equation of the Tangent Line to the Graph