> f:=x->7*x^3-sin(x)^3; > plot(f(x), x=-2..2); > (D@@2)(f)(x); > D[1,1](f)(x); > diff(f(x),x,x); > diff(f(x),x$2);The 2 in the first

> (D@@3)(f)(x); > D[1,1,1](f)(x); > diff(f(x),x,x,x); > diff(f(x),x$3);In order to substitute an value into the higher order derivative the

> evalf(subs(x=0,diff(f(x),x,x,x))); > (D@@3)(f)(0); > D[1,1,1](f)(0);Remember from your work with the first derivative that the

> g:=19*x^5-14*x+100; > D(g)(x); > diff(g,x);

- Given the function:

**A.**- Enter as a function
**B.**- Plot the function on the interval
**C.**- Find the fifth order derivative using the
**D**command. **D.**- Find the fifth order derivative using the
**diff**command. **E.**- 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.

- A ball is thrown upward and its distance in feet is given as a function of seconds.

**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?

2017-02-14