Find an equation of the line tangent to at if , , , and .

Question

Find an equation of the line tangent to  at  if  ,  ,  , and  .

Quizplus · Accepted Answer

To find the equation of the tangent line, we need to find the derivative of the given function and evaluate it at the point of tangency. Using the power rule of differentiation, we have:

f'(x) = 3x^2 - 6x + 2

Substituting x = 10 (the x-coordinate of the point of tangency) into the derivative, we get:

f'(10) = 3(10)^2 - 6(10) + 2 = 272

Therefore, the equation of the tangent line is:

y - 13 = 272(x - 10)

Simplifying and putting it in the desired form, we get:

y = 272x - 2717

Thus, the correct choice is B.

Find an Equation of the Line Tangent to at