For the function y=fx=√ 2x-5
Determine the average rate of change of y with respect to x from x=3 to x=5.
m = [ f(b) - f(a) ] / ( b - a )
If your question means:
f(x) =√ (2 x - 5 )
then
m = [ f(b) - f(a) ] / ( b - a )
m = [ f(5) - f(3) ] / ( 5 - 3 ) =
[ √ ( 2 ∙ 5 - 5 ) - √ ( 2 ∙ 3 - 5 ) ] / 2 =
[ √ ( 10 - 5 ) - √ ( 6 - 5 ) ] / 2 =
( √ 5 - √1 ) / 2 =
( √ 5 - 1 ) / 2 = 0.618033989
To determine the average rate of change of y with respect to x from x=3 to x=5, we need to find the difference in y values (Δy) divided by the difference in x values (Δx) for the given interval.
1. Substitute x=3 into the function:
f(3) = √(2(3) - 5) = √(6 - 5) = 1
2. Substitute x=5 into the function:
f(5) = √(2(5) - 5) = √(10 - 5) = √5
3. Calculate the difference in y values (Δy):
Δy = f(5) - f(3) = √5 - 1 = √5 - 1
4. Calculate the difference in x values (Δx):
Δx = 5 - 3 = 2
5. Calculate the average rate of change (ARC):
ARC = Δy / Δx = (√5 - 1) / 2
So, the average rate of change of y with respect to x from x=3 to x=5 is (√5 - 1) / 2.
To determine the average rate of change of y with respect to x from x=3 to x=5 for the given function y = √(2x - 5), we need to find the difference in y-values divided by the difference in x-values.
1. First, substitute x=3 into the function to find the corresponding y-value:
f(3) = √(2*3 - 5) = √(6 - 5) = √1 = 1
2. Next, substitute x=5 into the function to find the corresponding y-value:
f(5) = √(2*5 - 5) = √(10 - 5) = √5
3. Calculate the difference in y-values:
Δy = √5 - 1
4. Calculate the difference in x-values:
Δx = 5 - 3 = 2
5. Finally, calculate the average rate of change:
Average Rate of Change = Δy / Δx = (√5 - 1) / 2
So, the average rate of change of y with respect to x from x=3 to x=5 for the given function is (√5 - 1) / 2.