The graphs of three functions f(x), g(x) and h(x) are given below . Determine fo
ID: 2845650 • Letter: T
Question
The graphs of three functions f(x), g(x) and h(x) are given below . Determine for each function which graph corresponds to the functions 1st (1, 2, or 3) and 2nd (a, b, or c) derivatives. Also, explain (in paragraph form) how you determined your answer.
Explanation / Answer
f(x): first derivative 2, second derivative c; this is because the slope of f(x) begins at the left very positive, rolls over to zero and becomes slightly negative, and flattens out (to zero) just as it crosses the origin. The slope on the positive side of the y-axis is the mirror image of the negative side. These characteristics match first derivative graph 2. The same analysis applied to graph 2 matches second derivative graph c.
g(x): first derivative 3, second derivative b; the slope of g(x) starts out negative, becomes zero slightly to the left of the y-axis, and goes positive. This matches first derivatve curve 3. And since that curve is basically a straight line, second derivative curve b is right.
h(x): first derivative 1, second derivative a; same reasoning, starts out negative, slope becomes a little positive going through the y-axis, then negative again. Matches curve 1.
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