Calculus Derivatives and Calculator Functions

This tutorial demonstrates how to calculate derivative function values using the TI-89 graphing calculator. It covers two examples: a polynomial function and a trigonometric function. The video explains how to use the calculator's differentiate function, adjust settings for radian mode, and perform substitutions to find specific derivative values. The tutorial emphasizes the importance of correct mode settings and provides step-by-step instructions for entering functions and interpreting results.

What is the function given in the first example of the tutorial?

• f(x) = 1/2 x^2 - 5x + 4

• f(x) = x^2 + 5x - 4

• f(x) = 1/2 x^2 + 5x - 4

• f(x) = x^2 - 5x + 4

Which key combination is used to clean up the screen on the TI-89 calculator?

• F3, Option 2

• F6, Second, F1, Option 2

• F1, Option 1

• F2, Option 3

What is the derivative function f'(x) for the first example?

• f'(x) = 2x - 5

• f'(x) = x - 5

• f'(x) = 2x + 5

• f'(x) = x + 5

What is the value of f'(3) in the first example?

• 8

• 10

• 9

• 7

What is the value of f'(4) in the first example?

• 11

• 8

• 9

• 10

What is the function given in the second example of the tutorial?

• g(x) = 2 cos(x)

• g(x) = 2 tan(x)

• g(x) = 2 sin(x)

• g(x) = 2 sec(x)

Which mode should the calculator be in for trigonometric functions?

• Radian and Auto

• Degree and Auto

• Degree and Exact

• Radian and Exact

What is the derivative function g'(x) for the second example?

• g'(x) = 2 sin(x) sec(x)

• g'(x) = 2 cos(x) tan(x)

• g'(x) = 2 sec(x) tan(x)

• g'(x) = 2 sin(x) cos(x)

What is the value of g'(π/3) in the second example?

• 2√3

• 3√3

• 5√3

• 4√3

What is the value of g'(0) in the second example?

• 0

• 3

• 1

• 2