Ch3 Unit Test AP Calc // Alaysha Burrell

Question 1

Instantaneous Velocity

Answer 1

V(t)=S’(t)

Question 2

y’(cosx)

Answer 2

-sinx

Question 3

y’(tanx)

Answer 3

sec^2x

Question 4

y’(cotx)

Answer 4

-csc^2x

Question 5

y’(secx)

Answer 5

secxtanx

Question 6

Horizontal Tangent

Answer 6

dy/dx = 0

Question 7

Non-Differentiable Functions

Answer 7

1) No continuity
2) Corner
3) Cusp
4) Vertical Tangent Line

Question 8

Average Rate of Change (msec)

Answer 8

[f(b)-f(a)]/(b-a) . . . (or w/time)

Question 9

Displacement (Change in Position)

Answer 9

ΔS=S(t2)-S(t1)

Question 10

Product Rule f(x)g(x)

Answer 10

f(x)g’(x)+g(x)f’(x)

Question 11

Sum/Difference Rule f(x) +/- g(x)

Answer 11

f’(x)+/-g’(x)

Question 12

Quotient Rule f(x)/g(x)

Answer 12

[g(x)f’(x)-f(x)g’(x)]/(g(x))^2

Question 13

Product Rule kf(x)

Answer 13

kf’(x)

Question 14

y’(sinx)

Answer 14

cosx

Question 15

y’(cscx)

Answer 15

-cscxcotx

Question 16

Tangent Line

Answer 16

Find Derivative

Question 17

Normal Line

Answer 17

Same point, different slope (perpendicular)

Question 18

Differentiable Functions

Answer 18

1) Is it continuous? Yes: Continue. No: DNE.
2) Find Left and Right-Hand Derivatives
3) Left and Right-Hand Derivatives have to equal to be differentiable

Question 19

Notation for Derivatives

Answer 19

First: y’
Second: y’’
Third: y’’’
Fourth: y^(4)
So on…

Question 20

Instantaneous Rate of Change (mtan)

Answer 20

f’(x)

Question 21

Motion Along A Coordinate Line (Position)

Answer 21

S(t)

Question 22

Average Velocity

Answer 22

Vav= [S(t2)-S(t1)]/(t2-t1)

Question 23

Speed

Answer 23

Abs(v(t))

Question 24

Acceleration

Answer 24

A(t)=v’(t)=s’‘(t)