Question

The curve ascends in quadrant 3 from left parenthesis negative 2 comma negative 5 right parenthesis, intersects the x-axis into quadrant 2 at left parenthesis negative 1.7 comma 0 right parenthesis, and peaks at left parenthesis negative 1 comma 4 right parenthesis. The curve then descends and crosses the origin and forms a valley at left parenthesis 0.5 comma negative 1.7 right parenthesis. It then rises to intersect the x-axis into quadrant 1 at left parenthesis 1 comma negative 0 right parenthesis. The curve extends upward through quadrant 1 and passes through left parenthesis 1.4 comma 5 right parenthesis. All values are approximate.Which of the following most accurately identifies the relative maximum and minimum of the polynomial function h(x)?(1 point)ResponsesThere is a relative maximum at x=1.5and a relative minimum at x=−2.There is a relative maximum at x equals 1.5 and a relative minimum at x equals negative 2 .There is a relative maximum at x=−1and a relative minimum at x=0.555.There is a relative maximum at x equals negative 1 and a relative minimum at x equals 0.555 .There is a relative maximum at x=−1and no relative minimum.There is a relative maximum at x equals negative 1 and no relative minimum.There is a relative minimum at x=−1and a relative maximum at x=0.555.

Answer 1

Correct choice: There is a relative maximum at x = −1 and a relative minimum at x = 0.555.

Reason: The graph has a peak at (−1, 4) (local maximum) and a valley at about (0.5, −1.7) (local minimum), so the option giving a max at x = −1 and a min near x = 0.5 (listed as 0.555) is the best match.