Question

Consider the functions:

f(x) = x2


g(x) = (x + 1)2 – 2


h(x) = (x + 3)2 + 4


Which statement describes the relationship between the minimums of the functions?


a The minimum of h(x) is farther left and up than the minimum of f(x) and g(x).

b The minimum of g(x) is in the fourth quadrant. The minimum of h(x) is in the first quadrant.

c The minimum of g(x) is farther right and down than the minimum of f(x) and h(x).

d The minimum of g(x) is in the second quadrant. The minimum of h(x) is in the first quadrant.

Answer 1

The first one on edge2020. Just got it right.

Explanation:

So the person above is correct :)

Answer 2

a The minimum of h(x) is farther left and up than the minimum of f(x) and g(x)

Explanation:

To know the relation between the minima of the functions you calculate the minima by using the derivative:

`f'(x)=2x\\\\g'(x)=2(x+1)\\\\h'(x)=2(x+3)`

to find the values of x you equal the derivative of the function to zero:

`f'(x)=0;\ x=0;\\\\g'(x)=0; \ x=-1;\\\\h'(x)=0;\ x=-3;`

by evaluating this values of x you obtain the coordinates of the minima:

`f(0)=0\\\\g(-1)=-2\\\\h(-3)=4`

hence, the coordinates will be:

f -> (0,0)

g -> (-1,-2)

h -> (-3,4)

hence, the relation is:

a The minimum of h(x) is farther left and up than the minimum of f(x) and g(x).