__Question 1:__

**True or False**. An absolute maximum or minimum must occur at a critical point or at an endpoint.

__Answer :__

True.

__Question 2:__

**True or False**. To find the linear approximation to a function at x = a you need to know the first derivative of that function.

__Answer :__

True. The linear approximation L(x) to a function f(x) is given by

L(x) = f(a) + (x - a) f '(a) , where f ' is the derivative of f

__Question 3:__

**True or False**. Newton's method is used to approximate the extrema of a function.

__Answer :__

False. Newton's method is used to approximate the zeros of a function.

Note: If the first derivative of f is known, then yes Newton's method can be used to find the zero of the derivative which is the location of an extremum of function f.

__Question 4:__

**True or False**. Newton's methods fails if f '(a) is equal to zero and a is used as an initial value in the iteration process.

__Answer :__

True.

__Question 5:__

**True or False**. L'Hopital's rule states that the limit of a function of the form f(x) / g(x) is equal to the limit of the derivative of

f(x) / g(x).

__Answer: __

False. L'Hopital's rule states that the limit of a function of the form f(x) / g(x) is equal to the limit of

f '(x) / g '(x).

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