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Math
Calculus
F(x) derivatives
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Terms in this set (12)
If f(x) is increasing at x=c then f'(x)
The y value of f' is positive
If f(x) is decreasing at x=c then f'(x)
The y value of f' is negative
If f(x) is concave up at x=c (increasing and bent up) then f'(x)
F' is increasing at x=c (slope is positive)
If f(x) is concave up at x=c (increasing and bent up) then f"(x)
The y value if f" is positive
If f(x) is concave down at x=c (decreasing and bent down) then f'(x)
F' is decreasing at x=c (negative slope)
If f(x) is concave down at x=c (decreasing and bent down) then f"(x)
The y value of f" is negative
If f(x) has a relative minimum at x=c (horizontal tangent line, slope changes negative to postitive) then f'(x)
F'(c)=0 and has negative values to the left and positive to the right
If f(x) has a relative minimum at x=c (horizontal tangent line, slope changes negative to postitive) then f''(x)
Then f"(c) >0
If f(x) has a relative maximum at x=c (horizontal tangent line, slope changes positive to negative ) then f'(x)
F'(c)=0 and positive y values to the left and negative to the right
If f(x) has a relative maximum at x=c (horizontal tangent line, slope changes positive to negative ) then f''(x)
F"(c) is negative
If f(x) has a point of inflection at x=c (change in concavity) then f'(x)
Has a relative min or max at x=c
If f(x) has a point of inflection at x=c (change in concavity) then f''(x)
F"(c)= 0 and changes sign, values to the immediate left and right have different signs
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