Which of the following is true regarding a concave function?Group of answer choicesIt has a single global minimumIt is bowl-shaped upIt is relatively difficult to maximizenone of the above

A quadratic function is concave if the coefficient of every squared term is negative and there is no cross term of decision variables.Group of answer choicesTrueFalse

Consider the function f:R2→R𝑓:𝑅2→𝑅 defined byf(x,y)=x2+bxy+y2+alogcosh(x)𝑓(𝑥,𝑦)=𝑥2+𝑏𝑥𝑦+𝑦2+𝑎log⁡cosh⁡(𝑥)where a≥0𝑎≥0 and b𝑏 are real parameters. (a) If a=0𝑎=0, what is the smallest value of b𝑏 for which f𝑓 is convex?

The table gives values for a polynomial function 𝑔 at selected values of 𝑥. If 𝑎<𝑏, then 𝑔𝑎>𝑔𝑏 for all 𝑎 and 𝑏 in the interval 3<𝑥<7. Which of the following could be true about the graph of 𝑔 on the interval 3<𝑥<7 ?ResponsesThe graph of 𝑔 is concave down because the function is decreasing, and the average rate of change over equal-length input-value intervals is increasing.The graph of  g  is concave down because the function is decreasing, and the average rate of change over equal-length input-value intervals is increasing.The graph of 𝑔 is concave up because the function is decreasing, and the average rate of change over equal-length input-value intervals is increasing.The graph of  g  is concave up because the function is decreasing, and the average rate of change over equal-length input-value intervals is increasing.The graph of 𝑔 is concave down because the function is decreasing, and the average rate of change over equal-length input-value intervals is decreasing.The graph of  g  is concave down because the function is decreasing, and the average rate of change over equal-length input-value intervals is decreasing.The graph of 𝑔 is concave up because the function is decreasing, and the average rate of change over equal-length input-value intervals is decreasing.

For what interval of x-values is the curve y = f (x) concave up?

Which of the two functions below has the smallest minimum y-value?f(x) = 4(x - 6)4 + 1g(x) = 2x3 + 28A.The extreme minimum y-value for f(x) and g(x) is −∞−∞B.g(x)C.f(x)D.There is not enough information to determineSUBMITarrow_backPREVIOUS