SOLUTION: Determine all possible values of a such that the average rate of change of the function h(x)=x^2+3x+2 on the interval -3 ≤x ≤a is -1.
Algebra.Com
Question 1203974: Determine all possible values of a such that the average rate of change of the function h(x)=x^2+3x+2 on the interval -3 ≤x ≤a is -1.
Found 3 solutions by math_tutor2020, MathLover1, ikleyn:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
The average rate of change (AROC) is the same as the slope of the line through endpoints (-3,h(-3)) and (a,h(a))
If x = -3, then,
h(x) = x^2+3x+2
h(-3) = (-3)^2+3(-3)+2
h(-3) = 2
If x = a, then,
h(x) = x^2+3x+2
h(a) = a^2+3a+2
From here we conclude that a = -1 must be the case if we want the slope to be -1.
The average rate of change of h(x) = x^2+3x+2 on the interval is -1
Graph
Parabola h(x) = x^2+3x+2 in red
The line y = -x-1 is in green
The line passes through the points (-3,2) and (-1,0); both of which are on the parabola.
This line has a slope of -1 to represent the AROC on the interval
Desmos and GeoGebra are two graphing options I recommend.
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Answer: -1
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
on the interval
the average rate of change of the function
average rate=
in your case and
average rate=
Answer by ikleyn(52802) (Show Source): You can put this solution on YOUR website!
.
In the post by @MathLover1 EVERYTHING is INCORRECT,
in EACH LINE, starting from line #3 to the end.
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