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How do you find all values of x for which the function f is increasing?
Smalls108
You need to find all values of x for which the first derivative of the function is greater than zero.
Example: f(x)=x^2+5x+6
f'(x)=2x+5 = 0
x=-5/2
Consider intervals (minus infinity, -5/2) and (-5/2, infinity). Choose any number in each interval and examine the sign of f'(x), that is 2x+5. If it is positive, the function increases on that interval. If it is negative, the function decreases on that interval.
In this case, the function increases on (minus infinity, -5/2) and decreases on (-5/2, infinity).
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11
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