Question

Consider the functions:

Answer 1

Answer:

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

Step-by-step 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).