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-Find the values of x where the tangent line is horizontal for

Question

Quizplus · Accepted Answer

To find where the tangent line is horizontal, we need to find the values of x where the derivative of the function is equal to 0. Taking the derivative of the given function, we get:

f'(x) = 3x^2 - 8x + 4

Setting this equal to 0 and solving for x, we get:

3x^2 - 8x + 4 = 0

Using the quadratic formula, we get:

x = (8 ± sqrt(8^2 - 4*3*4)) / (2*3)

x = (8 ± sqrt(16)) / 6

x = (4/3), (2/3)

Therefore, the horizontal tangent lines occur at x = 4/3 and x = 2/3.

The only answer choice that includes 2/3 is C, so the answer is C.

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