1) the function is increasing from [-2,2] and is decreasing from (-infinity, -2]U[2,infinity). the graph is increasing in the interval [-2,2] because it is in the positve are of the graph. f(x) is decreasing in the interval [-infinity, -2]U[2,infinity] because it is in the negative are of the graph.
2) the extrema are in the x=-2, and 2. these points are the extrema because it is where f'(x) = 0 and where there is a change with in the slope. at x=-2 the extrema is the local mininum and at x=2 the the extrema is the local maximum.
3) the graph is concave up from (-infinity, -1.25, ] U [0, 1.25] and concave down [-1.25, 0] U [1.25, infinity]
4) the graph looks like a cube function with a parabola in the sides.
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1. Looks good! If I were to be picky though, it should use (), not [] because the slope is 0, not positive or negative at the endpoints. Plus, I wouldn't include 0 either.
ReplyDelete2. Yup!
3. Great. If I were to be picky though, I would use (), not []. Why?
4. Hm. With four changes in slopes, I would say it looks like a fourth degree polynomial. Which means the antiderivative, f(x), could be...?