Consider the function
y = 5x^2 + x
1). The average rate of change of y with respect to x over the interval 0 ≤ x ≤1 is ?
2). The instantaneous rate of change of y with respect to x at x=1 is ?
- I appreciate any help.
The answer for 1) Isn't 1.75 and the answer for 2) Isn't 6.
Thanks
y = 5x^2 + x
1). The average rate of change of y with respect to x over the interval 0 ≤ x ≤1 is ?
2). The instantaneous rate of change of y with respect to x at x=1 is ?
- I appreciate any help.
The answer for 1) Isn't 1.75 and the answer for 2) Isn't 6.
Thanks
-
1.
y(0)=0
y(1)=6
=> Average ROC for [0-1] = (6-0)/(1-0) = 6
Think of the average rate of change over an interval as the slope of a line drawn between those two points on the curve.
2.
The instantaneous rate of change at x=1 is the derivative at that point
y = 5x^2 + x
=> y' = 10x + 1
==> y'(1) = 11
(Don't know how much calc you know but based on this question I'm assuming you know basic derivatives)
y(0)=0
y(1)=6
=> Average ROC for [0-1] = (6-0)/(1-0) = 6
Think of the average rate of change over an interval as the slope of a line drawn between those two points on the curve.
2.
The instantaneous rate of change at x=1 is the derivative at that point
y = 5x^2 + x
=> y' = 10x + 1
==> y'(1) = 11
(Don't know how much calc you know but based on this question I'm assuming you know basic derivatives)