Question

The curve descends steeply in quadrant 2 from left parenthesis negative 0.3 comma 4 right parenthesis, passes through the origin, then forms a valley in quadrant 4 at left parenthesis 0.5 comma negative 1.7 right parenthesis. The curve rises and passes through left parenthesis 1.25 comma negative 0.5, then curves rightward to intersect the x-axis into quadrant 1 at left parenthesis 2 comma 0 right parenthesis. It turns upward through quadrant 1 and passes through left parenthesis 3 comma 3 right parenthesis. All values are approximate.Carmen was asked to identify the relative extrema of the polynomial function h(x) . Which of the following statements should she make?(1 point)ResponsesThere is an absolute minimum at x=0.5 .There is an absolute minimum at x equals 0.5 .There is a relative maximum at x=0.5 .There is a relative maximum at x equals 0.5 .There is an absolute maximum at x=0.5 .There is an absolute maximum at x equals 0.5 .There is an absolute minimum at x=0.5 and a relative minimum at x=2 .

Answer 1

There is an absolute minimum at x = 0.5.

Reason: the point (0.5, −1.7) is a valley (lower than nearby values) and the ends of the polynomial rise, so this is the lowest point on the graph (global/absolute minimum).