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

First, we need to find the derivative of the function at the given point. Using the power rule, we have:
f'(x) = 3x^2 - 8x + 5
f'(2) = 3(2)^2 - 8(2) + 5 = 5

Next, we use the point-slope form of a line to find the equation of the tangent line. Given a point (a, b) and slope m, the equation of the line is:
y - b = m(x - a)

Substituting in the values we found earlier, we have:
y - 2 = 5(x - 2)
y - 2 = 5x - 10
y = 5x - 8

Therefore, the equation of the tangent line to the graph of the given function at the point (2, 2) is y = 5x - 8. Converting to the given format, the answer is choice C: 11eaa595_661c_e0e2_a696_b9118a5dfe2d_TB4584_11_TB4584_11.

Find an Equation of the Tangent Line to the Graph