1. Find the value of the absolute maximum of f(x) = 2x³- 3x²+ 36x on the interval [5, 5].Answers

A.

44.000

B.

36.500

C.

44.000

D.

15.236

2. Find the value of the absolute minimum off(x) = 2x³- 3x²+ 36x on the interval [5, 5].Answers

A.

145.000

B.

145.000

C.

15.236

D.

36.500

3. Given a polynomial function f(x) = ax³+ bx²+ cx + d, which of the following statements are true?Answers

A.

On the interval (a, b) the function f(x) must have an absolute maximum.

B.

On the interval [c, d] the function f(x) must have an absolute minimum.

C.

On the interval [c, d], if the function f(x)has an absolute maximum, then it must occur at a location where f '(x) = 0.

4.Suppose that the profit a company makes from selling x units of a product is given by P(x) = 2x²+ 600x - 100. If the company can produce 200 cans at most, how many should they sell in order to maximize the profit?Answers

A.

1500

B.

600

C.

150

D.

60

5.Rolle's Theorem can be applied to f(x) = x² on the interval [2, 5].Answers

A.

True

B.

False

6.The Mean Value Theorem guarantees you that on the interval [0, 4] the function f(x) = x²will at some point in the interval have a slope of ___.Answers

A.

0

B.

2

C.

4

D.

8

E.

none of these

7. The statement "If f(b) is a relative maximum on the interval [a, c] then f(b) will be the highest point on the plot of f(x) from x = a to x = c." is Answers

A.

always true.

B.

sometimes true.

C.

never true.

Question10.If f(b) is a relative minimum, which of the following will not be true for a point x = c?Answers

A.

At a point x = c, located just to the right of x = b, f(c) > f(b).

B.

At a point x = c, located just to the right of x = b, f '(c) > f '(b).

C.

At a point x = c, located just to the left of x = b, f(c) > f(b).

D.

At a point x = c, located just to the left of x = b, f '(c) > f '(b).

Question11.If f(x) is a continuous function with a critical number at c, then which of the following are true?Answers

A.

If f '(x) changes sign from positive to negative at c, then c is a maximum.

B.

If f '(x) changes sign from negative to positive at c, then c is a maximum.

C.

If f '(x) doesn't change sign as it passes through c, then c is a minimum.

Question12.When using critical numbers to check for possible relative maximums for the function f(x) = 2x³- 9x²+ 12x - 1 on the interval [0, 3], how many critical numbers will you have to check on?Answers

A.

0

B.

1

C.

2

D.

3

E.

more than 3

Question13.At a point where the second derivative of a function is negative, the tangent to the curve at that point willAnswers

A.

always be above the curve.

B.

always be below the curve.

C.

sometimes be above and sometimes be below the curve.

Question14.If a tangent line to a curve falls below the curve at the point of tangency, then the curveAnswers

A.

is concave down.

B.

is concave up.

C.

can be either concave down or concave up.

Question15.If the first derivative of a function is negative at a point x, then the curveAnswers

A.

is concave down at that point.

B.

is concave up at that point.

C.

can be either concave down or concave up at that point.

Question16.An inflection point can only occur at a point where the second derivative is zero or undefined.Answers

A.

True

B.

False

Question17.If the second derivative is zero, then you are always at an inflection point.Answers

A.

True

B.

False

Question18.If a function is at a relative maximum, then its second derivative will beAnswers

A.

positive.

B.

negative.

C.

zero.

Question19.If the limit of f(x) approaches 2 as x approaches infinity, then you are dealing withAnswers

A.

a horizontal asymptote.

B.

a vertical asymptote.

C.

an oblique asymptote.

D.

either a horizontal asymptote or a vertical asymptote.

Question20.If the limit of f(x) approaches infinity as x approaches 2, then you are dealing withAnswers

A.

a horizontal asymptote.

B.

a vertical asymptote.

C.

an oblique asymptote.

D.

either a horizontal asymptote or a vertical asymptote.