Questions: Which of the following is true for the function shown above. A Extrema =(3.47,-0.74) B Local Max =0.76 at x=-0.74 C Local Max =0 at x=5 D Local Max =-0.74 at x=0.76 E Local Max =-0.74 F Extrema =(0,0.6)

Solution Steps

A local maximum is a point on the graph where the function's value is greater than the values immediately surrounding it. Looking at the graph, we can see a "peak" around x = -1. Its y-value appears a bit above 0. Another candidate for a local maximum does not exist.

A local minimum is a point on the graph where the function's value is less than the values immediately surrounding it. The graph has a "valley" around x = 4. Its y-value appears to be slightly less than -1, close to -0.7 or -0.8

A. Extrema = (3.47, -0.74). The minimum looks close to x=4, not 3.47. The y-value seems plausible. This is unlikely.

B. Local Max = 0.76 at x=-0.74. The local max is around x = -1, not -0.74. The y-value also isn't accurate. This is incorrect.

C. Local Max = 0 at x=5. There's no maximum at x=5. This is incorrect.

D. Local Max = -0.74 at x = 0.76. This states that a maximum is around x = 0.76 which is false. The y-value is also wrong.

E. Local Max = -0.74. This states that the maximum value is negative, which is not true for local maxima. This is incorrect.

F. Extrema = (0, 0.6). If "extrema" includes both maximum and minimum points, this is incorrect as the graph seems to have a y-intercept close to 0.7 or 0.8. This is incorrect.

None of the provided options are entirely correct.

Final Answer