Find an equation of the tangent line for at x = 2.

Question

Find an equation of the tangent line for  at x = 2.

Quizplus · Accepted Answer

To find the equation of the tangent line, we need to find the derivative of the function first.
Taking the derivative of 11eaa88b_9163_359d_a696_9f3993bf2c4b_TB5869_11, we get 
dy/dx = 3x^2 -14x - 5.

Now, to find the slope of the tangent line at x=2, we substitute x=2 into the derivative:
dy/dx at x=2 = 3(2)^2 - 14(2) - 5 = -13

Thus, the slope of the tangent line at x=2 is -13. We can use point-slope form to get the equation of the tangent line:

y - 11 = (-13)(x - 2)

Simplifying, we get

y = -13x + 37

Therefore, the correct answer is B: 11eaa88b_9163_359f_a696_c5ea4127f574_TB5869_11.

Find an Equation of the Tangent Line for at X