Free Printable Concavity and Implicit Review

1.

The concavity of a function is described by its _______________.

a)

first derivative

b)

second derivative

c)

third derivative

d)

expression

2.

Find dy/dx by Implicit Differentiation
x³ +y³ = 36

a)

6 -x

b)

3x² +3y²

c)

−x²/y²

d)

0

3.

Find dy/dx by Implicit Differentiation
xy = 6

a)

-x/ y

b)

-y/ x

c)

-6y/ x

d)

y/x

4.

Find dy/dx (implicit derivative)

xy+y²=2

a)

-y/(x+2y)

b)

y/(x+2y)

c)

-3y/x

d)

-3x/y

5.

Plug (2, 1) into your derivative

a)

-2

b)

-2/3

c)

2/3

d)

2

6.

Find the second derivative of

f(x) = x²+ e^x - cosx

(normal e and cos rules)

a)

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

b)

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

c)

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

d)

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

7.

Find the derivative (normal product and e rule, 5x² would be your f):

y=5x²e^3x

a)

y'=10xe^3x+ 5x²e^3x

b)

y'=10xe^3x + 15x²e^3x

c)

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

d)

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

8.

Differentiate the function with respect to x.

y = ln (x +1)

a)

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

b)

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

c)

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

d)

$\frac{1}{x}$

9.

Differentiate the function with respect to x.

y = ln (7x +1)

a)

$\frac{7}{7x+1}$

b)

$\frac{7x+1}{x}$

c)

$\frac{1}{1-7x}$

d)

$\frac{1}{7x}$

10.

Differentiate the function with respect to x.

y = $\ln6x^4$

a)

$\frac{4}{x}$

b)

$\frac{1}{6x^4}\times24x\ =\frac{4}{x^3}$

c)

$\frac{1}{6x^4}\times24x^5\ =\frac{4x}{1}$

11.

Differentiate the function with respect to x.

y =ln $e^{5x}$

(tips: differentiate ln ,copy the exponential, then differentiate the index,)

a)

$5$

b)

$5xe^{5x}$

c)

$1$

12.

What is dy/dx?

y^3=6x

a)

$\frac{2}{y^2}$

b)

$\frac{3}{y^3}$

c)

$3y^2$

d)

$\frac{2x}{y^2}$

13.

The normal to the curve is

a)

the derivative

b)

the integral

c)

perpendicular to the tangent to the curve

d)

the tangent to the curve

14.

Find the derivative of $x^2+xy+y^3=0$

a)

$-\ \frac{2x}{1+3y^2}$

b)

$-\frac{x+3y^2}{2x+y}$

c)

$-\frac{2x+y}{x+3y^2}$

d)

$-\frac{2x}{x+3y^2}$

15.

Find the value of dy/dx at the point (1,1) if x + 2xy - y² = 2

a)

3/2

b)

1/2

c)

0

d)

-3/2

e)

Does Not Exist

16.

If $x^3+3xy\ +\ 2y^3=17\$ find dy/dx

a)

$-\frac{x^2+y}{x+2y^2}$

b)

$-\frac{x^2+y}{x+y^2}$

c)

$-\frac{x^2+y}{x+2y}$

d)

$-\frac{x^2+y}{2y^2}$

e)

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

17.

If the gradient of the tangent is $\frac{4}{3}$ , what is the gradient of the normal at the same point?

a)

$-\frac{3}{4}$

b)

$\frac{4}{3}$

c)

$\frac{3}{4}$

d)

$-\frac{4}{3}$

18.

Find dy/dx
xy+y²=2

a)

-y/(x+2y)

b)

y/(x+2y)

c)

-3y/x

d)

-3x/y

19.

Find dy/dx by Implicit Differentiation
x³ +y³ = 36

a)

6 -x

b)

3x² +3y²

c)

−x²/y²

d)

0

20.

If $y^3+y\ =\ x^2$ find y'

a)

y' = 0

b)

y' = $\frac{x}{2}$

c)

y' = $\frac{2x}{3y^2}$

d)

y' = $2x-3y^2$

e)

y' = $\frac{2x}{1+3y^2}$

21.

Find the slope of the line tangent to the curve $y^2+\left(xy+1\right)^3=0$ at $\left(2,-1\right)$

a)

$-\frac{3}{2}$

b)

$-\frac{3}{4}$

c)

$\frac{3}{4}$

d)

$\frac{3}{2}$

22.

a)

-3

b)

8

c)

0

d)

9

23.

What is the oldest form of long-distance communication humans have used for sending messages?

a)

The telegraph

b)

The Pony Express

c)

Messenger pigeons

d)

voicemail

24.

Which one is a pigeon?

a)

b)

c)

d)

25.

Who wrote 'Pigeons'?

a)

Shakespeare

b)

Richard Kell

c)

Carol Ann Duffy

d)

Miss D herself

Concavity and Implicit Review

Total questions: 25

Worksheet time: 1hrs 15mins

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