Just for fun

Question 1

If a function f(x) has a relative minimum at x = 6, what does this tell us about the sign of its derivative f'(x) around x = 6?

Accepted Answer

0

Question 2

A particle moves along the x-axis. If its velocity is given by v(t) = t^2 - 5t + 4, when does the particle reach its leftmost point?

Accepted Answer

1

Question 3

Consider the function f(x) = x^3 - 3x on the interval [0, 1]. What is the absolute maximum value of this function?

Accepted Answer

0

Question 4

If a differentiable function f(x) has a critical number at x = -6 and f'(x) is negative to the left of -6 and positive to the right of -6, what type of extremum occurs at x = -6?

Accepted Answer

0

Question 5

True or False: A function can have an absolute maximum at a point where its derivative is zero.

Accepted Answer

o

Question 6

The function f(x) = x^3 - 2x^2 + 5 has critical numbers where f'(x) = 0. What are these critical numbers?

Accepted Answer

1

Question 7

If f'(x) > 0 for all x in an interval, what can be said about the function f(x) on that interval?

Accepted Answer

2

Question 8

True or False: Every continuous function on a closed interval has an absolute minimum.

Accepted Answer

o

Question 9

Consider the data table provided. At x = -6, f(x) = -8 and f'(x) = 0. At x = -4, f(x) = -6 and f'(x) = 3. What can be determined about the extremum at x = -6?

Accepted Answer

1

Question 10

The velocity of a particle is given by v(t) = t^2 - 5t + 4. If the particle starts at position x = 0 at t = 0, where is the particle at t = 5?

Accepted Answer

2

# 1

Multiple Choice

If a function f(x) has a relative minimum at x = 6, what does this tell us about the sign of its derivative f'(x) around x = 6?

# 2

Multiple Choice

A particle moves along the x-axis. If its velocity is given by v(t) = t^2 - 5t + 4, when does the particle reach its leftmost point?

# 3

Multiple Choice

Consider the function f(x) = x^3 - 3x on the interval [0, 1]. What is the absolute maximum value of this function?

# 4

Multiple Choice

If a differentiable function f(x) has a critical number at x = -6 and f'(x) is negative to the left of -6 and positive to the right of -6, what type of extremum occurs at x = -6?