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The slope of the function is most positive either side of x=0 and x=2π.
On the interval [0, π/4], the average slope is
On the interval [7π/4, 9π/4], the average slope is
The average rate of change is highest on the intervals [0, π/4] and [7π/4, 9π/4].
On the interval [0, π/4], the average slope is
On the interval [7π/4, 9π/4], the average slope is
The average rate of change is highest on the intervals [0, π/4] and [7π/4, 9π/4].
Your answer would be 18.1 cm.
To find this length you have to notice that AC is the hypotenuse of the right-angled triangle ACD. This means that we can find it by using Pythagoras' Theorem (a² + b² = c²), however we need to find the length CD.
We can also find the length CD using Pythagoras' Theorem, because the length CD is the same as the base of the triangle at the top if the shape was split into a rectangle and a triangle.
The height of this triangle would be 11 - 4 = 7 cm, which means we can find CD by doing:
16² - 7² = 256 - 49 = 207 = CD²
Now we can find AC by doing √(CD² + 11²) = √(207 + 121) = √368 = 18.1
I hope this helps! Let me know if you have any questions :)
