Answer:
- local maximum: (-5, 345)
- local minimum: (2, 2)
Explanation:
You want the local extremes of f(x) = 2x³ +9x² -60x +70.
Graph
A graphing calculator makes short work of this. Most can tell you the locations and values of the extremes. Here, we have ...
- local maximum: (-5, 345)
- local minimum: (2, 2)
Calculus
If you'd like to find these by hand, you can locate the turning points by finding the zeros of the derivative.
f'(x) = 6x² +18x -60 = 6(x² +3x -10)
f'(x) = 6(x +5)(x -2)
The turning points are located at x=-5 and x=2, where the derivative function is zero.
The values of f(x) at those points are ...
f(-5) = ((2(-5) +9)(-5) -60)(-5) +70 = (-1(-5) -60)(-5) +70 = (-55)(-5) +70 = 345
f(2) = ((2(2) +9)(2) -60)(2) +70 = (13(2) -60)(2) +70 = -34(2) +70 = 2
The local maximum is (-5, 345); the local minimum is (2, 2).
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