Question

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

f(x)=x^5-2
g(x)=3x^2+1

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)

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,

`(d)/(dx)`f(x)=
`5x^(4)`

Take
`(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,

`(d)/(dx)`g(x)=
`6x^(1)`

Take
`(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)