Use the function below and its derivative to determine any points on the graph of $f$ at which the tangent line is horizontal.
$$f ( x ) = - 2 x ^ { 4 } + 4 x ^ { 2 } , f ^ { \prime } ( x ) = - 8 x ^ { 3 } + 8 x$$
A) $( - 1,2 ) , ( 0,0 ) , ( 1,2 )$
B) $( - 1 , - 2 ) , ( 1 , - 8 )$
C) $( - 1,2 ) , ( 1,2 )$
D) $( 0,0 ) , ( 1,0 )$
E) $( 0,0 ) , ( 1,2 )$

Question

Quizplus · Accepted Answer

The tangent line is horizontal where the derivative $f'(x) = 0$. Solving $f'(x) = -8x^3 + 8x = 0$ gives $x = 0, \pm 1$. Substituting these values into $f(x)$ gives the points $(-1, 2), (0, 0), (1, 2)$.

Use the Function Below and Its Derivative to Determine Any fff

Use the Function Below and Its Derivative to Determine Any $f$