`f(x) = 6sin(x) - x^2, -5<=x<=3` Produce graphs of `f` that reveal all the important aspects of the curve. In particular, you should use graphs of `f'` and `f''`

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gsarora17 eNotes educator| Certified Educator

`f(x)=6sin(x)-x^2`

DomainĀ `-5<=x<=3`

`f'(x)=6cos(x)-2x`

`f''(x)=-6sin(x)-2`

Refer the graphs plotted in several ranges for clarity (attached image and links). f(x) plotted in red color,f'(x) in blue color and f''(x) in green color.

From the graph,

Absolute Maximum at x `~~` 1.2

Absolute Minimum at x=-5

Local Maximum at x `~~` -2.94

Local Minimum at x `~~` -2.66

Inflection points at x `~~` -2.8 , x`~~` -0.35

The function is concave up on the interval about (-2.8,-0.35)

The function is concave down in the intervals about (-5,-2.8) and (-0.35,3)

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