Answer:
C
Step-by-step explanation:
Find the average rate of change in each option:
A. For [tex]-2\le t\le 0:[/tex]
[tex]\dfrac{h(0)-h(-2)}{0-(-2)}\\ \\=\dfrac{((0+3)^2+5)-((-2+3)^2+5)}{2}\\ \\=\dfrac{(9+5)-(1+5)}{2}\\ \\=\dfrac{14-6}{2}\\ \\=4[/tex]
Positive
B. For [tex]1\le t\le 4:[/tex]
[tex]\dfrac{h(4)-h(1)}{4-1}\\ \\=\dfrac{((4+3)^2+5)-((1+3)^2+5)}{3}\\ \\=\dfrac{(49+5)-(16+5)}{3}\\ \\=\dfrac{54-21}{3}\\ \\=11[/tex]
Positive
C. For [tex]-4\le t\le -3:[/tex]
[tex]\dfrac{h(-3)-h(-4)}{-3-(-4)}\\ \\=\dfrac{((-3+3)^2+5)-((-4+3)^2+5)}{1}\\ \\=\dfrac{(0+5)-(1+5)}{1}\\ \\=\dfrac{5-6}{1}\\ \\=-1[/tex]
Negative
D. For [tex]-3\le t\le 4:[/tex]
[tex]\dfrac{h(4)-h(-3)}{4-(-3)}\\ \\=\dfrac{((4+3)^2+5)-((-3+3)^2+5)}{7}\\ \\=\dfrac{(49+5)-(0+5)}{7}\\ \\=\dfrac{54-5}{7}\\ \\=7[/tex]
Positive
