Weird precalculus problem?
I don't get this it at all. It says "find the average rate of change for the function between the given values."
F(x)=8x^3+6x^2-2; from 5 to 8
Update:Is the answer 11 or 1110? Thanks everyone for your input.
I don't get this it at all. It says "find the average rate of change for the function between the given values."
F(x)=8x^3+6x^2-2; from 5 to 8
Update:Is the answer 11 or 1110? Thanks everyone for your input.
Comments
average rate of change is a fancy way of saying 'slope between two points. Plug in 5, and you will get a point.... plug in 8, and you will get a point. Find the slope between them.
F(5) = 8(5)³ + 6(5)² -2
F(5) = 8(125) + 6(25) -2
F(5) = 1000 + 150 -2
F(5) = 1148
So one of the points is (5,1148)
F(8) = 8(8)³ + 6(8)² -2
F(8) = 8(512)+ 6(64) -2
F(8) = 4096+ 384 -2
F(8) = 4178
So our other point is (8,4178)
Recall the slope formula:
m = (y-Y)/(x-X)
m= (4178 - 1148) / (8-5)
-X)
m= 3330/ 3 = 1110
hope this helped.
this question wants you to find the slope of the line (secant) connecting the point in a function when x is 5 and 8
so you substitute 5 in for x to find the y value
y= 1000+150-2 = 1148
so, the first point is (5, 1148)
then you substitue 8 for x to find the y value of the second point
y=4096+384-2 = 4478
so the second point is (8, 4478)
since you got both points use slope = change in y /change in x
slope = (4478-1148)/(8-5)=3330/3 = 1110
1110 is the rate of change
This wants u to calculate the average rate by which the gradient changes between the x values 5 and 8. Esentialy ur answers's units wil be gradient units per unit in the x axis. So what u do is find the derivative of the function then substitute 5 into the derivative then u. Do the same thing wit 8. Then find the diference in the two answers this is ur change in gradient. Now u divide ur change in gradient by 3 to get the change in gradient per unit in the x axis since 8 - 5 is 3. Kinda lyk a distance time graph.
The rate of change compares how much f(x) changes to how much x changes.
f(8) = 8 * 8³ + 6 * 8² - 2 = 4096 + 384 - 2 = 4478
f(8) = 8 * 5³ + 6 * 5² - 2 = 1000 + 150 - 2 = 1148
[ f(8) - f(5) ] / (8 - 5) = (4478 - 1148) / (8 - 5) = 333 / 3 = 11
8(8)^3 + 6(8)^2 - 2 -(8(5)^3 + 6(5)^2 - 2) = 3330
3330/ (8-5) = 1110
This is the average rate of change per unit
pretty soon you will most likely get into derivatives and then you can find the exact rate of change.
That, I believe, is the slope of the line connecting the coords (5, y) and (8, y)
The y coords have to be found in order to find the slope . . . difference in y / difference in x.