Part of the graph of a function `f`, where `a>0`, is shown below.
The average value of the function `f` over the interval `[2a, a]` is
- `0`
- `a/3`
- `a/2`
- `3a/4`
- `a`
Calculus, MET2 2013 VCAA 15 MC
Let `h` be a function with an average value of 2 over the interval `[0, 6].`
The graph of `h` over this interval could be
Show Worked Solution
`text(Draw the line)\ \ y=2\ \ text(on each graph.)`
♦♦♦ Mean mark 25%.
`=>\ text(An average value of 2 occurs when the same area)`
`text(is enclosed above and below the graph.)`
`text(Consider)\ C,`
`text(Area)\ A =\ text(Area)\ B`
`=> C`
Calculus, MET2 2015 VCAA 8 MC
The graph of a function `f:\ text{[−2, p]} -> R` is shown below.
The average value of `f` over the interval `text{[−2, p]}` is zero.
The area of the shaded region is `25/8.`
If the graph is a straight line, for `0 <= x <= p`, then the value of `p` is
A. `2`
B. `5`
C. `5/4`
D. `5/2`
E. `25/4`
Calculus, MET2 2014 VCAA 20 MC
The graph of a function, `h`, is shown below.
The average value of `h` is
- `4`
- `5`
- `6`
- `7`
- `10`
Show Worked Solution
`text(From inspection, the average value of)\ h`
♦ Mean mark 44%.
`text(is either 6 or 7.)`
`h_text(avg) = 7\ text(as area bounded by)\ h(x)`
`text(and)\ y = 7\ text(above)\ y = 7\ text(is equivalent)`
`text(to area bounded below)`
`=> D`