Let . Find the derivative of and the point on the graph of where the tangent line to the curve is horizontal.

Question

Let  . Find the derivative  of  and the point on the graph of  where the tangent line to the curve is horizontal.

Quizplus · Accepted Answer

To find the derivative of the given function, we need to use the power rule for differentiation.

11eaa8b1_dc3e_0073_b1b6_cd727f9f9b45_TB6026_11 can be written as y = 11x^4.

Using the power rule, we get:

y' = 44x^3

Therefore, the derivative of 11eaa8b1_dc3e_2785_b1b6_f59ccdecc1ea_TB6026_11 is:

11eaa8b1_dc3e_0074_b1b6_7d455e4b3bb0_TB6026_11 = 44x^3

To find the point on the graph where the tangent line is horizontal, we need to find the value of x that makes the derivative equal to zero.

44x^3 = 0

Solving for x, we get:

x = 0

Therefore, the point on the graph where the tangent line is horizontal is when x = 0.

Substituting x = 0 in the original function, we get:

11eaa8b1_dc3e_2786_b1b6_17e64ccaf210_TB6026_11 = 11(0)^4 = 0

So the point on the graph is (0, 0).

Therefore, the final answer is D.

Let Find the Derivative of and the Point