Find the points on the curve $y = 2 x ^ { 3 } + 3 x ^ { 2 } - 36 x + 19$ where the tangent is horizontal.
A) $( - 3,100 ) , ( 2 , - 25 )$
B) $( - 3,88 ) , ( 4,39 )$
C) $( - 4,71 ) , ( 4,39 )$
D) $( - 4,71 ) , ( 2 , - 37 )$
E) $( - 3,37 ) , ( 2 , - 37 )$

Question

Quizplus · Accepted Answer

The tangent is horizontal when the derivative is zero. The derivative of the given function is $y' = 6x^2 + 6x - 36$. Setting this equal to zero and solving for x gives x = -3 and x = 2. Plugging these values back into the original function gives the points (-3, 100) and (2, -25).

Find the Points on the Curve y=2x3+3x2−36x+19y = 2 x ^ { 3 } + 3 x ^ { 2 } - 36 x + 19y=2x3+3x2−36x+19

Find the Points on the Curve $y = 2 x ^ { 3 } + 3 x ^ { 2 } - 36 x + 19$