Answer:
Average rate of change = -4
Step-by-step explanation:
Given:
f(x) = x² + 7x + 10
-8 ≤ x ≤ -3 or [-8, -3] in interval notation
Average rate of change of the function can be solved using the formula:
[tex]\mathrm{Average\:rate\:of\:change} = \dfrac{ f \left( b \right) -f \left( a \right) }{ b-a }[/tex]
[tex]\mathrm{Average\:rate\:of\:change} = \dfrac{ f \left( -3 \right) -f \left( -8 \right) }{ -3 - (-8) }[/tex]
[tex]\mathrm{Average\:rate\:of\:change} = \dfrac{ f \left( -3 \right) -f \left( -8 \right) }{ -3 + 8 }[/tex]
[tex]\mathrm{Average\:rate\:of\:change} = \dfrac{ f \left( -3 \right) -f \left( -8 \right) }{ 5 }[/tex]
Substitute x = -3 to the given function for f(-3) and x = -8 for f(-8)
[tex]\mathrm{Average\:rate\:of\:change} = \dfrac{ f \left( -3 \right) -f \left( -8 \right) }{ 5 }[/tex][tex]\mathrm{Average\:rate\:of\:change} = \dfrac{ { \left[( -3 \right) }^{ 2 } +7 \left( -3 \right) +10]- { \left[( -8 \right) }^{ 2 } +7 \left( -8 \right) +10] }{ 5 }[/tex]
[tex]\mathrm{Average\:rate\:of\:change} = \dfrac{ [9-21+10]-[64-56+10] }{ 5 }[/tex]
[tex]\mathrm{Average\:rate\:of\:change} = \dfrac{ [-2]-[18] }{ 5 }[/tex]
[tex]\mathrm{Average\:rate\:of\:change} = \dfrac{ - 20 }{ 5 }[/tex]
[tex]\mathrm{Average\:rate\:of\:change} = {-4 }[/tex]
