Exercises

1. Given the function:
   
   $$f(x)=2\cos(x)-\frac{x^5}{5}-10$$
   
   

   A)

   Plot the function on the interval $-2\leq x \leq 2$

   B)

   Plot the first derivative and then use Maple's solve command to find $x$ values where the first derivative is zero. Use the plot of the derivative to determine itervals where $f$ is increasing and decreasing.

   C)

   Plot the second derivative. About where does the second derivative graph cross the x-axis? Knowing that the second derivative represents concavity explain why your second derivative plot makes sense in conjunction with the plot of the original function.

2. A ball is thrown upward and its distance in feet is given as a function of seconds.
   
   $$s(t)=6+80t-16t^2$$
   
   

   A)

   Enter the function

   B)

   What is the initial velocity of the ball?

   C)

   When will the ball reach its maximum height?

   D)

   What is the highest point?

   E)

   What is the acceleration at any time?

3. Use a linear approximation to $f(x)=\sqrt{x}$ at $x=1$ to appproximate $\sqrt{2}$.