1. By using differential rules how can you expand your understanding of the example below if you have to evaluate f ' (a) and graph the f(x) and the tangent line at x = a

[T]f(x)=2x³+3xx² , a=2

2. Using the real-life example below solve the question by applying Derivatives as Rates of Change

[T]A profit is earned when revenue exceeds the cost. Suppose the profit function for a skateboard manufacturer is given byP (x) = 30x0.3x²250,where xis the number of skateboards sold.

2.1 Find the exact profit from the sale of the thirtieth skateboard.

2.2 Find the marginal profit function and use it to estimate the profit from the sale of the thirtieth skateboard.

3. Solving the example below explaining each step in your answer for maximum credit by applying derivatives of Trig functions.

The number of times a movie has been downloaded is given byy=16+3sinx where y is the number of downloads and x, represents the number of hours after the 1st movie was downloaded at 6 a.m. until 6 p.m when the downloads have stopped. Findyand determine the intervals where the number of downloads is increasing.