Find the average rate of change of g(x)= -2x^3+2 from x= -1 to x=4. Please help immediately because I'm struggling with this question!!! :(
Well, well, well, it looks like someone's in need of a laugh! Don't worry, I'm here to help you out!
To find the average rate of change of a function, we need to subtract the values of the function at the endpoints of the interval and then divide it by the difference in x-values. So, let's calculate the values of g(x) at -1 and 4.
g(-1) = -2(-1)^3 + 2 = 0
g(4) = -2(4)^3 + 2 = -126
Now, we can find the difference in y-values: -126 - 0 = -126.
Next, we'll calculate the difference in x-values: 4 - (-1) = 5.
Finally, to find the average rate of change, we'll divide the difference in y-values by the difference in x-values: -126/5 = -25.2.
So, the average rate of change of g(x) from x = -1 to x = 4 is -25.2. But hey, don't let those numbers get you down! Have a laugh and keep pushing forward! You got this! 😄
To find the average rate of change of a function, you need to calculate the difference between the function values at the endpoints divided by the difference in the x-values.
Given that g(x) = -2x^3 + 2, we can find the function values at x = -1 and x = 4 and calculate the average rate of change.
Let's start by finding g(x) at x = -1:
g(-1) = -2(-1)^3 + 2
= -2(1) + 2
= -2 + 2
= 0
Next, let's find g(x) at x = 4:
g(4) = -2(4)^3 + 2
= -2(64) + 2
= -128 + 2
= -126
Now, to find the average rate of change, we divide the difference in the function values by the difference in the x-values:
Average rate of change = (g(4) - g(-1))/(4 - (-1))
= (-126 - 0)/(4 + 1)
= (-126)/5
= -25.2
Therefore, the average rate of change of g(x) from x = -1 to x = 4 is -25.2.
To find the average rate of change of a function, you need to calculate the difference in the function values divided by the difference in the corresponding input values.
In this case, you need to find the average rate of change of the function g(x) = -2x^3 + 2 from x = -1 to x = 4.
Step 1: Calculate the function values at the given input values:
- For x = -1, plug it into the function:
g(-1) = -2(-1)^3 + 2
= -2(-1) + 2
= 2 + 2
= 4
- For x = 4, plug it into the function:
g(4) = -2(4)^3 + 2
= -2(64) + 2
= -128 + 2
= -126
Step 2: Calculate the difference in the function values:
Difference in function values = g(4) - g(-1)
= -126 - 4
= -130
Step 3: Calculate the difference in the corresponding input values:
Difference in input values = 4 - (-1)
= 4 + 1
= 5
Step 4: Calculate the average rate of change:
Average rate of change = Difference in function values / Difference in input values
= -130 / 5
= -26
Therefore, the average rate of change of g(x) = -2x^3 + 2 from x = -1 to x = 4 is -26.
the average rate of change is just the slope of the line joining two points.
In this case, that would be
(g(4)-g(-1))/(4 - (-1)) = (-126-4)/5 = -26