Question

Please Help!

Consider continuous functions f, g, h, and k. Then complete the statements.
*image*
Select the correct answer from each drop-down.
- The function that has the least minimum value is function ( g, h, k, f ).
- The function that has the greatest minimum value is function ( k, g, h, f ).

Answer 1

the least minimum value = k(x)

the greatest minimum value = h(x)

Explanation:

based on the graph, the minimum value for f(x) = -7

based on the table, the minimum value for g(x) = -5

h(x) = 2(x-1)²

= 2x²-4x+2

since coefficient of x² is positive, therefore the extreme point of h(x) has the minimum value:

`\boxed{y=-(b^2-4ac)/(4a) }`

`=-((-4)^2-4(2)(2))/(4(2))`

`=0`

k(x) = x⁴+2x²+8x-4

to find extreme points → k'(x) = 0

k'(x) = 4x³ + 4x + 8

0 = 4x³ + 4x + 8

0 = x³ + x + 2

x = -1

k(-1) = (-1)⁴+2(-1)²+8(-1)-4

= -9

Therefore, the least minimum value = k(x)

the greatest minimum value = h(x)