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Thank you for answering my question, it is very challenging (for me)!

I am given a table of information; on the left hand sign are a pair of f''(x) values and on the right a corresponding "+" or "-" sign. Use this table to find where the function is concave up or down and any inflection points.

(-infinity,10) accompanied by a "+" sign

(-10,2) accompanied by a "-" sign

(2,4) accompanied by a "+" sign

(4,10) accompanied by a "+" sign

(10,infinity) accompanied by a "-" sign.

It is known that where f"(x) is positive, the curve is concave up and

where f"(x) is negative, the curve is concave down.

For example, take f(x) = x^2, so f'(x) = 2x and f"(x) = 2.

This an be seen to have a positive f"(x) for all x, so it is concave up.

It can be seen that this curve is concave up on (-infinity,-10) { drop a minus sign??),

(2,4), and (4,10). It is concave down on (-10,2) and (10,infinity).

Since the intervals (2,4) and (4,10) both have the curve being concave up,

there is most likely an inflection point inbetween.

Calculus

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