Chapter 17 Multiple choice questions

. What is the maximum number of turning points or inflections in a graph of the form:

y = 2 x^{6} + 3 x^{5} + 7 x^{4} - 3 x^{3} + 5 x^{2} - 4 x + 8

.

6

5

4

3

. Determine the turning point of the following function:

y = x^{2} + 5 x + 6

.

(- 2 \frac{1}{2}, - 12 \frac{3}{4})

(- 2 \frac{1}{2}, - 9)

(- 2 \frac{1}{2}, - 12)

(- 2 \frac{1}{2}, - \frac{1}{4})

. Determine the turning point of the following function:

y = 3 x^{2} - 4 x - 10

.

(\frac{2}{3}, - 11 \frac{1}{3})

(\frac{- 2}{3}, - 6)

(\frac{- 2}{3}, - 11 \frac{1}{3})

(\frac{2}{3}, 6)

. Determine the turning points of the following function:

y = 4 x^{3} - 48 x

.

(2, - 64)

(2, - 64)

and

(- 2, 64)

(2.3, - 61.9)

and

(- 2, 64)

(- 2.3, 61.9)

and

(2, - 64)

. Determine the turning points of the following function:

y = 2 x^{4} + 216 x

.

(-3, 702)

(3, 810)

(-3, 486)

(3, -486) and (3, 810)

. At a minimum, the second differential of a function of the form

y = a x^{n} + b x^{n - 1} + ...

is

positive.

negative.

zero.

infinite.

. Write down the double differential of:

y = 9 x^{2} - 4 x + 3

.

\frac{d^{2} y}{d x^{2}} = - 18 x - 4

\frac{d^{2} y}{d x^{2}} = - 4

\frac{d^{2} y}{d x^{2}} = 22

\frac{d^{2} y}{d x^{2}} = 18

. Find the turning point of the following function and determine whether it is a maximum, minimum, or inflection point:

y = - 6 x^{2} + 48 x + 15

.

(4, 111)—a minimum

(4, 111)—a maximum

(4, -273)—a minimum

(4, -273)—a maximum

. Find the turning point of the following function and determine whether it is a maximum, minimum, or inflection point:

y = \ln (4 x^{3}) - 3 x^{5}

.

(0.725, -0.179)-a maximum

(0.725, -0.179)-a minimum

(-0.725, 0.179)-a maximum

(-0.725, -0.179)-a minimum

. Find the first turning point (x > 0) of the following function and determine whether it is a maximum, minimum, or inflection point:

y = \cos (4 x)

.

(\frac{3 π}{4}, 1)

—a maximum

(\frac{3 π}{4}, - 1)

—a minimum

(\frac{π}{4}, - 1)

—a minimum

(\frac{π}{4}, 1)

—a maximum

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