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 $c 0 , f ( x ) = c x ^ { 4 } + 5 x ^ { 2 } + 1$, opens upward with two minimum points. For $c 0 , f ( x ) = c x ^ { 4 } - 5 x ^ { 2 } + 1$, opens upward with two minimum points. For $c 0 , f ( x ) = c x ^ { 4 } - 5 x ^ { 2 } + 1$, opens upward with two minimum points. For $c 0 , f ( x ) = c x ^ { 4 } + 5 x ^ { 2 } - 1$, opens downward with two maximum points. For $c

Question

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 $x = 0$.

Quizplus · Accepted Answer

For $c=0$, the function simplifies to a downward-opening parabola with a maximum at $x=0$. For $c>0$, the function is a quartic polynomial that opens upward, typically having two minimum points due to the negative quadratic term. For $c<0$, the function opens downward, with $x=0$ being a point of local maximum, not having any local minimum points.

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

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