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

What can you say about point of inflation for f(x)=xe−3x ? \text { What can you say about point of inflation for } f ( x ) = x e ^ { - 3 x } \text { ? } What can you say about point of inflation for f(x)=xe−3x ?

Multiple Choice