For What Values Of $c$ Does the Curve Have Maximum and Minimum Points for the and Minimum

Multiple Choice

For what values of $c$ does the curve have maximum and minimum points for the given function $f ( x ) = c x ^ { 4 } - 5 x ^ { 2 } + 1 ?$
Select the correct answer.

A) For $c = 0 , f ( x ) = - 5 x ^ { 2 } + 1$ , a parabola whose vertex $( 0,2 )$ , is the absolute maximum.
For $c > 0 , f ( x ) = c x ^ { 4 } - 5 x ^ { 2 } + 1$ , opens downward with one minimum points.
For $c < 0$ , the graph opens upward, and has an absolute maximum at $x = 0$ and no local minimum.

B) For $c = 0 , f ( x ) = 5 x ^ { 2 } + 1$ , a parabola whose vertex $( 0,2 )$ , is the absolute maximum.
For $c > 0 , f ( x ) = c x ^ { 4 } + 5 x ^ { 2 } + 1$ , opens upward with two minimum points.
For $c < 0$ , the graph opens downward, and has an absolute minimum at $x = 0$ and no local minimum.

C) For $c = 0 , f ( x ) = 5 x ^ { 2 } + 1$ , a parabola whose vertex $( 0,3 )$ , is the absolute maximum.
For $c > 0 , f ( x ) = c x ^ { 4 } - 5 x ^ { 2 } + 1$ , opens upward with two minimum points.
For $c < 0$ , the graph opens downward, and has an absolute minimum at $x = 0$ and no local minimum.

D) For $c = 0 , f ( x ) = - 5 x ^ { 2 } + 1$ , a parabola whose vertex $( 0,1 )$ , is the absolute maximum.
For $c > 0 , f ( x ) = c x ^ { 4 } - 5 x ^ { 2 } + 1$ , opens upward with two minimum points.
For $c < 0$ , the graph opens downward, and has an absolute maximum at $x = 0$ and no local minimum.

E) For $c = 0 , f ( x ) = - 5 x ^ { 2 } + 1$ , a parabola whose vertex $( 0 , - 1 )$ , is the absolute maximum.
For $c > 0 , f ( x ) = c x ^ { 4 } + 5 x ^ { 2 } - 1$ , opens downward with two maximum points.
For $c < 0$ , the graph opens upward, and has an absolute minimum at $x = 0$ .