1. Function Increasing (-2,-1)U(0,1) here the slope is increasing; Function Decreasing (-1,0)U(1,2) because the slope is decreasing . Also because f '(x) is the derivative of f(x) and the derivative is the slope of the original function.
2. Local Extrema local maximum x=+1 and x=-1 there the slope was positive and then had a flat slope to turn negative. local minimum x=0 there the slope was negative then reach to a slope of 0 and then switch to a positive slope making a critical point.
3. Concave up between (-1,1) where it looks like it can hold water. Concave down is (-2,-1)U(1,2) where it looks like its going to spill water.
4. x^3+x^2 is f(x) on the given slopes and concavity shows it as the two power function are combined.
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1. =( YOu want to look for where f'>0 or where the graph itself is ABOVE the x-axis, because there the outputs are positive. It's asking you for where f is increasing or decreasing, not f'.
ReplyDelete2. Sorry, this one was my fault in not clarifying that again, I was looking for the extrema of f, not f'.
3. This one, however, was clear that I'm not looking for where the graph of f' (that you see) is concave up, but where f' (that you don't see) is concave up.
4. This can't be a cubic because it has 4 changes in slopes. The minimum power function this can be is a fourth degree polynomial, making the function itself, f(x), a 5th degree in the least.