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 the derivative of the function at the given point. Using the power rule of differentiation, we have:

f'(x) = 4x^3 - 12x^2 + 7x - 4
f'(1) = 4(1)^3 - 12(1)^2 + 7(1) - 4 = -5

So the slope of the tangent line is -5.

Using the point-slope form of a line, we can write:

y - 1 = (-5)(x - 2)

y = -5x + 11

Therefore, the equation of the tangent line at the point (2, 1) is y = -5x + 11, which is choice C.

Find an Equation of the Line Tangent to at