Free Printable pre test

1.

What is the maximum value of f(x) = x³ - 3x² - 1 on the interval [-3, 2]?

a)

0

b)

-1

c)

2

d)

5

2.

Find the open interval(s) where the function is increasing:

f\left(x\right)=-x^3-10x^2-32x-32

a)

$\left(-\infty,-\frac{4}{3}\right),\left(-\frac{8}{9},\infty\right)$

b)

$\left(-4,-\frac{8}{3}\right)$

c)

$\left(-\infty,-4\right),\left(-\frac{8}{3},\infty\right)$

d)

$\left(-16,-\frac{32}{3}\right)$

3.

Find the second derivative of the function:
f (x) = 2x - 5x⁶

a)

f ''(x)= 2 - 30x

b)

f ''(x) = 2-30x⁵

c)

f ''(x) = -30x⁵

d)

f ''(x) = -150x⁴

4.

Identify the critical points of the following function:
g(x)=2x³-3x²

a)

x=-1,1

b)

x=0,0

c)

x=0,-1

d)

x=0,1

5.

On what interval(s) is the function $f\left(x\right)=x^3+6x^2$ concave down?

a)

$\left(-\infty,-4\right)$

b)

$\left(-\infty,-2\right)$

c)

$\left(-2,\infty\right)$

d)

$\left(0,\infty\right)$

6.

The value of c guaranteed to exist by the MVT for $f\left(x\right)=x^2$ on the interval [0,3] is:

a)

1

b)

2

c)

3/2

d)

1/2

7.

Pick a function which is continuous in the given interval.

a)

y = cot(x) [-π,2π]

b)

y = $\frac{x^2+5x+3}{x-1}\ \ \ \ \ \ \left[0,3\right]$

c)

y = $\left(7x^2+6x-3\right)\left(x^6-3x+7\right)\ \ \ \ \ \ \ \ \left[2,9\right]$

d)

y = $\frac{\sin\left(x\right)}{x-1}\ \ \ \ \ \ \ \ \ \left[0,4\right]$

8.

For what value of c is the Rolle's thm applicable on the given function f(x) = x²-5x+4 [1,4]

a)

c = 7/2

b)

c = 5/2

c)

c = 3/2

d)

c = 9/2

9.

Verify L.M.V Theorem for the $f\left(x\right)=x^3\ \ \ \ \ \left[-1,3\right]$ and find c.

a)

$c=\pm\sqrt{\frac{7}{3}}$

b)

$c=\pm\sqrt{\frac{3}{7}}$

c)

$c=\sqrt{\frac{7}{3}}$

d)

$c=-\sqrt{\frac{3}{7}}$

10.

$critical\ point\ \ \ for\ f\left(x\right)\ =\frac{2-x}{1-x}$

a)

2,1

b)

-2,1

c)

2,-1

d)

none

11.

Find the intervals of concavity for

f(x) = x² + 2x + 1.

a)

concave up: (-∞,∞)

b)

concave down: (-∞,∞)

c)

concave up: (2, ∞)

concave down: (-∞,2)

d)

concave up: (-∞,2)

concave down: (2, ∞)

12.

Find the relative minimum values for f(x)=3x⁴-2x³-9x²

a)

-1

b)

0

c)

1.5

d)

-1 and 1.5

13.

Find the critical points of f(x) = 2x⁴- 4x² + 1

a)

x= 0

b)

x = -1, 1

c)

x = -1, 0, 1

d)

no critical points

14.

Write 1 + 2 + 3 + ... + 10

using sigma notation

a)

$\sum_{d=1}^9d$

b)

$\sum_{d=1}^{10}d+1$

c)

$\sum_{d=1}^{10}d$

15.

write the sums $\sum_{n=1}^6\left(2n-1\right)$

a)

1, 3, 5, 7, 9, 11

b)

1, 2, 3, 4, 5, 6

c)

1+2+3+4+5+6

d)

1+3+5+7+9+11

16.

a)

b)

c)

d)

17.

a)

b)

c)

d)

18.

∫₁³ 5x² dx

a)

a. 43

b)

b. 130/3

c)

c. 40

d)

d. 19/3

19.

What is the value of the definite integral : $\int_{-3}^3x^2+x+1\ dx$ ?

a)

6

b)

9

c)

24

d)

33

20.

$\int_{-2}^{-1}\ \left(4x^2\ +\ 3x\ -1\right)\ dx$ =

a)

$\frac{89}{6}$

b)

$\frac{23}{6}$

c)

7

d)

0

pre test

Total questions: 20

Worksheet time: 2hrs 40mins

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