Free Printable 4/9 Calculus Honors Period 1 Asynchronous Assignment

1.

What can you conclude from this number line?

a)

there is a maximum for A at 12

b)

there is a minimum for A at 12

c)

you will have a profitable year

d)

the stars are aligning nicely

2.

A rectangle is bounded by the x-axis and the parabola $y=12-x^2$ . What equation for the derivative should the rectangle have so that its area is a maximum?

a)

$A'=2xy$

b)

$A'=\ \ 24-6x^2$

c)

$A'=2x\left(12-x^2\right)$

d)

$A'=12-2x$

3.

A farmer wants to construct a rectangular pigpen using 400 ft of fencing. The pen will be built next to an existing stone wall, so only three sides of fencing need to be constructed to enclose the pen. What dimensions should the farmer use to construct the pen with the largest possible area?

a)

100ft x 200ft

b)

102ft x 196 ft

c)

50 ft x 300 ft

d)

50 ft x 175 ft

4.

Use the sign chart for f'(x). There is(are) ...

a)

a local maximum at x = -2.

b)

a local minimum at
x = -2 and a local maximum at x = 4.

c)

a local maximum at
x = -2 and a local minimum at x = 4.

d)

no extrema.

5.

a)

A

b)

B

c)

C

d)

D

6.

Identify the interval from the derivative graph where the function is concave up.

a)

(-1,1) & (3,4)

b)

(-3,-2)

c)

(-2,-1)

d)

(-3,-1) & (1,3)

7.

a)

A

b)

B

c)

C

d)

D

e)

E

8.

The function f has a local Max at x = ?

a)

-3

b)

-1

c)

1

d)

3

e)

4

9.

What are the x-coordinates of the Points of Inflection of the graph of f ?

a)

0 only

b)

3 only

c)

0 and 6 only

d)

3 and 6 only

e)

0, 3, and 6

10.

Let f be the function with derivative given by f'(x) = x² - 2/x. On which of the following intervals is f decreasing?

a)

(-∞, 0]

b)

(-1, 0]

c)

(0, ∛2]

d)

(∛2, ∞)

11.

Over what intervals is f(x) decreasing?

a)

(-∞, -1) ∪ (1, ∞)

b)

(-∞, -√3) ∪ (0, √3)

c)

(-1, 1)

d)

(-√3, 0) ∪ (√3, ∞)

12.

If $\ f'\left(x\right)=x^2+7$ , which of the following could be f(x)? (given that c is any number)

a)

$2x$

b)

$\frac{x^3}{3}+7x+c$

c)

$x^3+7x+c$

d)

$\frac{x^4}{8}+c$

13.

Given that $f'\left(x\right)=5x^4$ , which of the following could be f(x) where c could be any number.

a)

$x^5$

b)

$\frac{5}{4}x^5+C$

c)

$x^5+C$

d)

$20x^3$ + C

14.

Given that $f'\left(x\right)=\ 5x^2-7x+6$ , determine which equation could be the equation for f(x). (c represents any number)

a)

$\frac{5}{3}x-\frac{7}{2}x+6x+C$

b)

$x+x+x+x+x+C$

c)

$x^3-3x^2+6x+C$

d)

$\frac{5}{3}x^3-\frac{7}{2}x^2+6x+C$

15.

If $\ f'\left(x\right)=\frac{7}{x}$ , which of the following could be f(x)?

a)

$\frac{-7}{x^2}$

b)

$\ln\left(7x\right)$

c)

$-7$

d)

$7\ln x$

16.

Given that $f'\left(x\right)=6x\left(x+2\right)$ , which of the following could be f(x) given that c is any number

a)

$6x^2+12x+C$

b)

$x^{2\ }-2x+C$

c)

$3x^2+6x+C$

d)

$2x^3+6x^2+C$

17.

Given that $f'\left(x\right)=\sin x$ which of the following could be f(x).

a)

$f\left(x\right)=\cos x+1$

b)

$f\left(x\right)=-\cos x+1$

c)

$f\left(x\right)=\cos x+x$

d)

$f\left(x\right)=-\cos x+x$

18.

a)

A.

b)

B.

c)

C.

d)

D.

19.

Find the derivative:
y=5x²e^3x

a)

y'=10xe^3x(2x+3)

b)

y'=5xe^3x(3x+2)

c)

y'=10ex^3x(3x+2)

d)

y'=5xe^3x(2x+3)

20.

Find the SECOND derivative of
f(x) = x²+ e^x - cosx

a)

f"(x) = 2 + e^x + cosx

b)

f"(x) = 2 + e^x - cosx

c)

f"(x) = 2x + xe^x - cosx

d)

f"(x) = 2x + e^x + sinx

21.

Evaluate $\frac{\text{d}}{\text{d}x}\left[\ln\left(\frac{x+1}{x}\right)\right]$ (Hint: use properties of logarithms prior to differentiating)

a)

$\frac{1}{x+1}-\frac{1}{x}$

b)

$\frac{x}{x+1}$

c)

$-\frac{1}{x^2}$

d)

$1+\frac{1}{x}$

22.

a)

-3

b)

8

c)

0

d)

9

23.

Find dy/dx at a given point. (NOTE: implicit differentiation)

a)

5/4

b)

4/5

c)

1

d)

-5

24.

Find dy/dx
sin(y²)=x

a)

1/(2ycos(y²))

b)

cos(y²)

c)

x/(2ycos(y²))

d)

-1/(cos(y²))

25.

Find the derivative of $f\left(x\right)=\ln\left(\frac{x^3\left(x+1\right)}{\sqrt{x^4+2}}\right)^{ }$ (hint: use the properties of logarithms first)

a)

$f'\left(x\right)=\frac{3}{x}+\frac{1}{x+1}-\frac{1}{2\left(x^4+2\right)}$

b)

$f'\left(x\right)=\frac{4x-3}{4x^3}$

c)

$f'\left(x\right)=\frac{x^3\left(x+1\right)}{\sqrt{x^4+2}}$

d)

$f'\left(x\right)=\frac{3}{x}+\frac{1}{x+1}-\frac{2x^3}{\left(x^4+2\right)}$

4/9 Calculus Honors Period 1 Asynchronous Assignment

Total questions: 25

Worksheet time: 2hrs 34mins

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