Expert: Scott A Wilson - 10/23/2009

Question
Hi, i have a couple questions i did them already but i do not know if i did them right.
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Find the intervals on which the given function is increasing and the intervals on which it is decreasing.

problem 59:
f(x)=x^2+1

problem 61:
f(x)=-3x+1

problem 63:
f(x)=-(x+2)^2-1
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Answer
The functions are increasing where they have a positive derivative and decreasing where they have a negative derivative.

For f(x) = x² + 1, f'(x) = 2x.  This is + for x>0 and - for x<0.
Therefore it can be said that f(x) is increasing for x>0 and decreasing for x<0.

For f(x)=-3x+1, f'(x)=-3, therefore the function is always decreasing.

For f(x)=-(x+2)²-1, f'(x)=-2(x+2)(1), for 1 is the derivative of x+2.
Since the function is f'(x) = -2x - 4, this is 0 at x = -2.
On the left side, the derivative is negative, which means function is decreasing,
and on the right side, the derivative is positive, which means the function is increasing.