1st and 2nd Derivative Rules Test
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8 Terms
1
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f(x) is increasing
f’(x) is positive, f’(x)>0
2
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f(x) is decreasing
f’(x) is negative, f’(x)<0
3
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f(x) is at a critical value
if f is defined, f’=0 or DNE
4
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f(x) is at a relative max
f’ changes from positive to negative at a critical value
f’’(C.V.)<0, if f’ exists and is differentiable
5
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f(x) is at a relative min
f’ changes from negative to positive at a critical value
f’’(C.V.)>0, if f’ exists and is differentiable
6
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f(x) is concave up
f’(x) is increasing
f’’(x) is positive, f’’(x)>0
7
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f(x) is concave down
f’(x) is decreasing
f’’(x) is negative, f’’(x)<0
8
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f(x) is at a point of inflection
f’(x) is at either a relative minimum or maximum
f’’(x)=0 or DNE and changes sign