**Question: **Let \(f\left( x \right)=2{{x}^{3}}-6x+7\).

(a) On what interval(s) is f(x) decreasing?

(b) On what interval(s) is f(x) concave up?

(c) What are the maximum and minimum values of f(x)?

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**Question: **A certain radioactive substance has a half-life of 23 years. For how long must the substance decay so that there is 18% of the original amount remaining? For full credit you must solve an appropriate equation.

**Question: **A farmer wants to enclose two congruent rectangular regions using 600 meters of fencing. Assuming that he wants to maximize the area, what are the dimensions for the fenced in area?

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**Question: **Find the vertex and axis of symmetry for the function \[f\left( x \right)=-{{x}^{2}}+4x+1\]

**Question: **A farmer uses 1200 feet of fence to enclose a rectangular region and also to subdivide the region into three smaller rectangular regions by placing fences parallel to one of the sides. Find the dimensions that produce the greatest enclosed area.

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**Question: **Determine the number of units \[x\] that produce a maximum profit for the profit function, \[P\left( x \right)=-\frac{{{x}^{2}}}{14,000}+1.68x-4000\]. Also, determine the maximum profit.

**Question: **Sketch the graph of the function: \(y={{x}^{3}}-6{{x}^{2}}+9x+2\)

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