Determine all values of x, (if any), at which the graph of the function has a horizontal tangent.
E) The graph has no horizontal tangents.

Question

Determine all values of x, (if any), at which the graph of the function has a horizontal tangent. 
E) The graph has no horizontal tangents.

Quizplus · Accepted Answer

To find the values of x where the function has a horizontal tangent, we need to find where the derivative of the function equals zero. Taking the derivative of the function, we get f'(x) = 8x^3 - 72x^2 + 216x - 204. Setting this equal to zero and solving for x, we get x = 1 or x = 3. Plugging these values back into the original function, we find that they correspond to the point (1, -24) and (3, 60). At these points, the function has a horizontal tangent since the derivative changes signs from negative to positive or positive to negative. Therefore, the answer is B.

Determine All Values of X, (If Any), at Which the Graph