10-11

Question 1

What is the derivative at x = a?

Answer 1

Instantaneous rate of change and slope of tangent line

Question 2

What is the four-step process for computing the derivative using the definition?

Answer 2

1. Identify f(a)
2. Compute f(a + h)
3. Find f(a + h) - f(a)
4. Take the limit as h approaches 0

Question 3

What is the derivative of a constant function f(x) = c?

Answer 3

f’(x) = 0

Question 4

What is the derivative of a linear function f(x) = cx?

Answer 4

f’(x) = c

Question 5

What is the derivative of the function f(x) = x^n?

Answer 5

f’(x) = nx^(n-1)

Question 6

What is the derivative of the function f(x) = cx^n?

Answer 6

f’(x) = ncx^(n-1)

Question 7

What is the derivative of sums or differences in functions?

Answer 7

If f(x) = u(x) + v(x), then f’(x) = u’(x) + v’(x)

Question 8

Fill in the blank: The derivative of a constant function is _______.

Answer 8

0

Question 9

True or False: The derivative of f(x) = cx^n is f’(x) = n * cx^(n-1).

Answer 9

True

Question 10

What is the formula for the derivative f’(a) using limits?

Answer 10

f’(a) = lim (f(a + h) - f(a)) / h as h approaches 0

Question 11

What does the derivative represent in calculus?

Answer 11

The instantaneous rate of change of a function