`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''`

Textbook Question

Chapter 4, 4.6 - Problem 6 - Calculus: Early Transcendentals (7th Edition, James Stewart).
See all solutions for this textbook.

1 Answer | Add Yours

gsarora17's profile pic

gsarora17 | (Level 2) Associate Educator

Posted on

`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)

Images:
This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)
Sources:

We’ve answered 318,936 questions. We can answer yours, too.

Ask a question