Three differentiable curves U, V, and W satisfy the following for every x.
1. U is increasing exactly where V is positive and decreasing exactly where V is negative.
2. V is increasing exactly where W is positive and decreasing exactly where W is negative.
3. W is negative on (−2,1) and positive on (−∞,−2)∪(1,∞).
4. V has zeros at x=−2 and x=1, and U has an inflection point at x=1.
Which identification of U, V, and W as f, f′, and f′′ is most consistent with these conditions?
a) U is f′,\; V is f′′,\; W is f
b) U is f′,\; V is f,\; W is f′′
c) U is f,\; V is f′,\; W is f′′
d) U is f′′,\; V is f,\; W is f′