The functions f and g are both defined on the interval (minus 5. 12). On this in

Question

The functions f and g are both defined on the interval (minus 5. 12). On this interval f is positive, decreasing, and concave up g is negative, increasing, and concave down. Let h(x) = f(x)^2+ g(x)^2 for x in the interval (minus 5, 12). Determine, if possible, whether h is increasing or decreasing on (minus 5, 12). If it is possible to make this determination, then state which is the case, with justification. If you cannot make the determination (i.e. you need more information) state this and tell what additional information you would need. Determine, if possible, whether h is concave up or concave down on (minus 5, 12). If it is possible to make this determination, then state which is the case, with justification. If you cannot make the determination (i.e. you need more information) state this and tell what additional information you would need.

Explanation / Answer

a)If g is increasing and concave down then g^2 is decreasing and concave up

Hence sum of decreasing functions is decreasing

Hence h is decreasing

B)It is concave up.

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