__Question 2:__

**True or False**. The sign of the first derivative of a given function f informs you on the interval(s) where f(x) is positive, negative or equal to zero.

__Answer :__

False.

The sign of the first derivative informs you on the interval(s) where f is increasing, decreasing or constant.

__Question 3:__

**True or False**. The sign of the second derivative of a given function f informs you on the concavity of the graph of f.

__Answer :__

True.

__Question 4:__

**True or False**. The horizontal asymptote to the graph of a given function f is determined by finding the limit, if it exists, of f(x) as x approaches 0.

__Answer :__

False.

A horizontal asymptote may be determined by finding the limit of f(x) as x approaches + or - infinity (very large or very small values).

__Question 5:__

**True or False**. Any value of x that makes the denominator of rational function f equal to zero, represents a vertical asymptote to the graph of f.

__Answer :__

False.

Not always. Let f(x) = (x + 3) / (x^{ 2} -9).

Factor the denominator and simplify to obtain f(x) = 1 / (x - 3)

Although x = - 3 makes the denominator equal to 0 there is no vertical asymptote at x = - 3; in fact there is a hole.

__Question 6:__

**True or False**. A horizontal asymptote may intersect the graph of the function.

__Answer :__

True.

Example: f(x) = sin x / x

__Question 7:__

**True or False**. The x intercepts of the graph of a function corresponds to the zeros of the function.

__Answer :__

True.

__Question 8:__

**True or False**. A graph cannot cut its vertical asymptote.

__Answer :__

True.

More references on calculus
questions with answers and tutorials and problems .