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Mean value Theorem help?
anyone able to help with the mean value theorem?
I have to find the point where instantaneous rate of change = average rate of change with f(x) = 3sin(2x) on [0, pi/4]
which means I need to find c, I found that f(c)' = 12/pi and f(x)' = 6cos(2x) which means 6cos(2x) = 12/pi
or cos(2x) = 2/pi
but then I have to graph it and none of the points are graph able as far as I can tell
1 Answer
- 2 years ago
(3 * sin(2 * pi/4) - 3 * sin(0)) / (pi/4 - 0) =>
3 * sin(pi/2) / (pi/4) =>
3 * 1 * 4 / pi =>
12/pi
So that works
f(x) = 3 * sin(2x)
f'(x) = 6 * cos(2x)
6 * cos(2x) = 12 / pi
cos(2x) = 2/pi
So that's good, too. Trust, but verify.
2x = arccos(2/pi)
x = (1/2) * arccos(2/pi)
x = 0.44034461771017833361347189128445......
x = 0.44 radians
y = cos(2x) - 2/pi
Find when y = 0, which is at 0.44 radians, which is in the domain.
