1. The function is increasing at (-2,0) and (0,2)
The function is decreasing at (-∞,-2) and (2,∞)
You can tell because at these intervals the outputs are the same as the slope of f(x). Increasing means the slope is positive and decreasing means the slope is negative.
2. There are possible extrema at the points x=-2, x=0, x=2 because at those points the output is zero.
3. At (-1,0) and (1,-∞) f(x) is concave down and at (-∞,1) and (0,1) f(x) is concave up because the slope of f'(x) is negative @ (-1,0) and (1,-∞) and positive @ (-∞,1) and (0,1).
4.The function is possibly either f(x)=sinx or f(x)=cosx.
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1. Excellent. 2. Not only can you tell there is a possible extrema, from this graph, you can tell exactly what they are. if f' changes from negative to positive, like at x=-2, there is a minimum. If f' changes from positive to negative, like at x=2, there is a max. However, if there is NO CHANGE of sign as in x=0, there is NEITHER a min or max.
ReplyDelete3. perfect.
4. not quite sin or cos because then it would look like the sin/cos curves exactly. this f' graph is a 4th degree equation so f has to be a 5th degree equation. possibly. =)