Question

Let h(x)=16 x+x²+73 Determine the absolute extrema of h on [-9,11]. The absolute minimum of h is ___ and it occurs at x= ___

Answer 1

To find the absolute extrema of h(x)=16x+x²+73 on the interval [-9,11], evaluate the function at the critical points and endpoints.

Step-by-step explanation:

To find the absolute extrema of the function h(x)=16x+x²+73 on the interval [-9,11], we need to evaluate the function at the critical points and endpoints of the interval. First, let's find the critical points by taking the derivative of h(x) and setting it equal to zero:

h'(x) = 16 + 2x = 0

2x = -16

x = -8

The critical point is x = -8. Now, we evaluate the function at x = -9, -8, 11:

h(-9) = 16(-9) + (-9)² + 73 = -144 + 81 + 73 = 10

h(-8) = 16(-8) + (-8)² + 73 = -128 + 64 + 73 = 9

h(11) = 16(11) + 11² + 73 = 176 + 121 + 73 = 370

The absolute minimum of h is 9 and it occurs at x = -8.