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 ->  Functions -> 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.      Log On


   

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) About Me  (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

slope+=+rise%2Frun



slope+=+%28h%28a%29-h%28-3%29%29%2F%28a-%28-3%29%29

slope+=+%28%28a%5E2%2B3a%2B2%29-%282%29%29%2F%28a%2B3%29

slope+=+%28a%5E2%2B3a%29%2F%28a%2B3%29

slope+=+%28a%28a%2B3%29%29%2F%28a%2B3%29

slope+=+%28a%2Across%28%28a%2B3%29%29%29%2F%28cross%28%28a%2B3%29%29%29

slope+=+a

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 -3+%3C=+x+%3C=+-1 is -1

Graph
graph%28400%2C400%2C-7%2C7%2C-7%2C7%2Cx%5E2%2B3x%2B2%2C-x-1%29
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 -3+%3C=+x+%3C=+-1
Desmos and GeoGebra are two graphing options I recommend.

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Answer: -1

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

+h%28x%29=x%5E2%2B3x%2B2 on the interval +-3+%3C=x+%3C=-1
the average rate of change of the function
average rate=+%28h%28a%29-h%28b%29%29%2F%28b-a%29
in your case +a=-3+ and++b=-1
+h%28-3%29=%28-3%29%5E2%2B3%28-3%29%2B2=9-9%2B2=2
+h%28-1%29=%28-1%29%5E2%2B3%28-1%29%2B2=1-3%2B2=0
average rate=+%282-0%29%2F%280-2%29=2%2F-2=-1

Answer by ikleyn(52798) About Me  (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.