The correct option is B). f(x)
The minimum value for y belongs to f(x) at x=0 and f(0)=(-2)
Step-by-step explanation:
The given two functions are f(x)=[tex]x^{5} -2[/tex] and g(x)=[tex]3x^{2} +1[/tex]
To find which function got minimum value for y :
For function f(x)=[tex]x^{5} -2[/tex]
Using concept of Maxima and Minima,
Function : f(x)=[tex]x^{5} -2[/tex]
Differentiating the function we get,
[tex]\frac{d}{dx}[/tex]f(x)=[tex]5x^{4} [/tex]
Take [tex]\frac{d}{dx}[/tex]f(x)=0
[tex]5x^{4}=0 [/tex]
x=0
Therefore, f(x)=f(0)=0-2=(-2)
For function g(x)=[tex]3x^{2} +1[/tex]
Using concept of Maxima and Minima,
Function : g(x)=[tex]3x^{2} +1[/tex]
Differentiating the function we get,
[tex]\frac{d}{dx}[/tex]g(x)=[tex]6x^{1} [/tex]
Take [tex]\frac{d}{dx}[/tex]g(x)=0
[tex]6x^{1} [/tex] =0
x=0
Therefore, g(x)=g(0)=0+1=1
Thus, The minimum value for y belongs to f(x) at x=0 and f(0)=(-2)
The correct option is B). f(x)
