Question

Which of the two functions below has the smallest minimum y-value?

Answer 1

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)=$x^{5} -2$ and g(x)=$3x^{2} +1$

To find which function got minimum value for y :

For function f(x)=$x^{5} -2$  

Using concept of Maxima and Minima,

Function : f(x)=$x^{5} -2$

Differentiating the function we get,

$\frac{d}{dx}$f(x)=$5x^{4}$

Take $\frac{d}{dx}$f(x)=0

$5x^{4}=0$

x=0

Therefore, f(x)=f(0)=0-2=(-2)

For function g(x)=$3x^{2} +1$

Using concept of Maxima and Minima,

Function : g(x)=$3x^{2} +1$

Differentiating the function we get,

$\frac{d}{dx}$g(x)=$6x^{1}$

Take $\frac{d}{dx}$g(x)=0

$6x^{1}$ =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)