ST 552

Calculus on a Computer

Assignment 3 – Derivatives

1. Let, and choose a point on the graph.

a. Sketch the graph of f, and draw the lines through the point at x=a and the point at x=a+h for h = 1, 0.5, 0.1, and sketch the tangent line.

b. Repeat with some negative h values.

c. Now draw the lines through the points at x=a-h and x=a+h.

d. Have MAPLE simplify the expression . What happens as h gets small? How does this relate to what you have done in the previous parts?

e. Use MAPLE to find the derivative of f(x).

f. What is the equation of the tangent line?

2. Repeat exercise1 for two other functions

3. Plot a polynomial in MAPLE, and choose a point on the graph. By choosing horizontal and vertical ranges, zoom in on the point. What do you observe?

4. Use MAPLE to find the derivative of your polynomial at the point. What is the equation of the tangent line? Plot the polynomial and the tangent line on the same graph and repeat exercise 3.

5. Repeat exercises 3 & 4 for a trig function.

6. Plot the following functions, and determine from the graph where the derivative is positive and where it is negative.

a.

b.

c.

d.

7. Now plot the derivatives of the functions in exercise 6 (use MAPLE) and see whether they agree with your answers.

8. Use the derivative of to find the tangent line to at the point (4, 2). Use this line to approximate . How close is your approximation?

9. Now use a tangent line to to approximate .