Sammy wrote the following proof. What did he do wrong?
2 answers:
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The functions in order from least to greatest according to their average rates of change are function f at the interval [1,2], function h at the interval [0,2] and function g at the interval [2,3]
<h3>How to order the functions?</h3>The rate of change is calculated using:
For function g at the interval [2,3], we have:
This gives
For function h at the interval [0,2], we have:
Where:
h(2) = 3(3)^2 - 9 = 18
h(0) = 3(3)^0 - 9 = -6
This gives
For function f at the interval [1,2], we have:
This gives
Hence, the functions are function f at the interval [1,2], function h at the interval [0,2] and function g at the interval [2,3]
Read more about average rates of change at:
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The correct answer is: [B]: " 
" .
__________________________________________________________
Consider choice [A]:
;
=
;
= 2 ; "2 ≠ -2" ; so we can rule out: "Choice [A]" .
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Consider choice [B]: ;
=
;
= "-2" ; Yes!
→ Let us proceed with the final answer choice ;
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Consider choice [C]:
;
= ;
= 2 ; "2 ≠ -2" ; so we can rule out: "Choice [C]" .
__________________________________________________________
The correct answer is: [B]: " " .
__________________________________________________________
__________________________________________________________
Consider choice [A]:
=
= 2 ; "2 ≠ -2" ; so we can rule out: "Choice [A]" .
__________________________________________________________
Consider choice [B]:
=
= "-2" ; Yes!
→ Let us proceed with the final answer choice ;
__________________________________________________________
Consider choice [C]:
=
= 2 ; "2 ≠ -2" ; so we can rule out: "Choice [C]" .
__________________________________________________________
The correct answer is: [B]: "
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