Given the function defined by y=x2+3 , what is its average rate of change from x = 2 to x = 5? PLEASE HELp
Please oh please help me
Im legit crying PLEASE
if x = 5, y = 5^2 + 3 = 25+ 3 = 28
if x = 2, y = 2^2 + 3 = 4 + 3 = 7
change in y = 28-7 = 21
change in x = 5 - 2 = 3
rate of change = dy/dx = 21/3 = 7
To find the average rate of change of a function between two points, we need to calculate the difference in the function's values divided by the difference in the x-values.
In this case, we have the function y = x^2 + 3. We want to find the average rate of change from x = 2 to x = 5.
Step 1: Find the function values at x = 2 and x = 5:
Let's substitute x = 2 and x = 5 into the function to get the corresponding y-values.
For x = 2:
y = (2)^2 + 3 = 4 + 3 = 7
For x = 5:
y = (5)^2 + 3 = 25 + 3 = 28
So, the function values at x = 2 and x = 5 are y = 7 and y = 28, respectively.
Step 2: Find the difference in y-values:
The difference in the y-values is the change in the function's values.
y2 - y1 = 28 - 7 = 21
Step 3: Find the difference in x-values:
The difference in the x-values is the change in the independent variable.
x2 - x1 = 5 - 2 = 3
Step 4: Find the average rate of change:
The average rate of change of the function is calculated by dividing the difference in y-values by the difference in x-values.
Average rate of change = (y2 - y1) / (x2 - x1) = 21 / 3 = 7
So, the average rate of change of the function y = x^2 + 3 from x = 2 to x = 5 is 7.