Xani L.

asked • 05/28/21# Calculus - Curve Sketching

A graph of the curve *y* = *f*(*x*) is shown below.

A point on the graph, where *f* '(*x*) < 0 and *f *''( *x*) < 0 is

- B
- D
- A
- C

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## 1 Expert Answer

- The first derivative tells us about the slope of the graph.
- If f'(x) is positive, the graph has a positive slope and is therefore increasing at x.
- If f'(x) is negative, the graph has a negative slope and is therefore decreasing at x.
- The second derivative tells us about the concavity of the graph.
- If f''(x) is positive, the graph is concave up.
- If f''(x) is negative, the graph is concave down.

Since both f'(x) and f''(x) are less than 0 (negative), look for a point where the graph is decreasing and concave down.

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Mark M.

Link is broken!05/29/21