A garden shop determines the demand function $q=D(x)=\frac{2 x+200}{10 x+11}$ during early summer for tomato plants where $q$ is the number of plants sold per day when the price is $x$ dollars per plant. (a) Find the elasticity. (b) Find the elasticity when $x=2$. (c) At $\$ 2$ per plant, will a small increase in price cause the total revenue to increase or decrease? (a) The elasticity is

Step 1 ：Given the demand function \(q=D(x)=\frac{2 x+200}{10 x+11}\), where \(q\) is the number of plants sold per day when the price is \(x\) dollars per plant.

Step 2 ：The elasticity of demand is a measure of how much the quantity demanded of a good responds to a change in the price of that good. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

Step 3 ：In this case, the elasticity of demand can be calculated using the formula: Elasticity = \((dq/dx) * (x/q)\), where \(dq/dx\) is the derivative of the demand function with respect to \(x\), \(x\) is the price, and \(q\) is the quantity demanded.

Step 4 ：First, we calculate the derivative of the demand function with respect to \(x\): \(dq/dx = -10*(2*x + 200)/(10*x + 11)^2 + 2/(10*x + 11)\).

Step 5 ：Then, we substitute the values of \(x\), \(q\), and \(dq/dx\) into the elasticity formula to get the elasticity of the demand function: \(x * (10*x + 11) * (-10 * (2*x + 200)/(10*x + 11)^2 + 2/(10*x + 11))/(2*x + 200)\).

Step 6 ：Final Answer: The elasticity of the demand function is given by \(\boxed{x \cdot \frac{(10x + 11) \cdot \left(-10 \cdot \frac{(2x + 200)}{(10x + 11)^2} + \frac{2}{10x + 11}\right)}{2x + 200}}\)