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Finding extrema / critical numbers?
Given: f(x) = x^3 - 3x^2 - 9x + 20
Find the local maximum point on the closed interval [-3, 5]
So f'(x) = 3x^2 - 6x - 9
f'(x) = 0 at x = 3 and x = -1
How do i find the maximum/minimums?
1 Answer
- ?Lv 76 years ago
Plug in x = 3, -1, -3 and 5 into the original function. The maximums and minimums can only occur at the endpoints and the critical points.
f(-3) = -7
f(-1) = 25
f(3) = -7
f(5) = 25
This means that there are (relative/local) minimums at x = -3 and 3 and relative/local maximums at x = -1 and x = 5.