You can differentiate at a point c if...

the limit of f'(c) is the same from both sides

You have a relative max when...

f'(x) change from postive to negative

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Duplicate of Calculus AP Review

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calculus term review

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Questions 30

Answers

1
You can differentiate at a point c if...
there is a cusp at c
there is a jump at c
the limit of f'(c) is the same from both sides
there is a vertical tangent at c
2
When finding volume perpendicular to the y-axis, your bounds & equations must in terms of...
x
huh?
z
y
3
What does this represent?
average velocity
blah
average acceleration
average position
4
Derivative of xⁿ is
xn+1/(n+1)
nxn-1
xn
nxn+1
5
You have a horizontal tangent line if...
dy/dx = 0
d2x/dy2 = 0
f(x) = 0
x = 0
6
This equals.... ???
f(g(x))
f(g(x))∙g'(x)
f(x) + C
f(t)
7
d/dx of x^1/2 is...
1/(2x)
(-1/2)x
1/2
1/(2x1/2)
8
A function is continuous at a 'c' if...
f(c) is defined
f(c) = limit as x approaches c
limit as x approaches c exisits
all the above
9
What does this represent?
average position
blah
average velocity
average acceleration
10
What does this represent?
total distance
0
acceleration
displacement
11
What does this represent?
displacement
acceleration
0
total distance
12
How do you find area between curves
both
none
∫(right - left)dy
∫(top - bottom)dx
13
How do you separate variables to find solutions?
integrate
derive
add or subtract
divide or multiply
14
What does this formula find??
slope
average rate of change
integral
average value of a function
15
You have a relative max when...
f(x) changes from positive to negative
f'(x) = 0
f'(x) change from postive to negative
f"(x) changes from postive to negative
16
You have a point of inflection when...
f"(x) = 0 & f"(x) changes sign
none of the above
f"(x) = 0 & slope of f'(x) changes sign
both of above
17
When you see "average rate of change on [a, b]" you should think...
all of the above
[ f(b) - f(a) ] / (b - a)
slope of the secant line
algebra slope
18
Derivative of 1/x
-1/x2
1/x2
x0/0
ln(x)
19
Particle is speeding up because...
v > 0 & a > 0
both of the above
none of the above
v < 0 & a < 0
20
What are you being asked to find?
integral
find 0's
derivative
limit
21
Instantaneous Rate of Change of f at a:
calculus slope
all of the above
slope of tangent line
f'(a)
22
Product Rule for f(x)g(x) is...
gf' - fg'
gf' + fg'
f'∙g'
multiplication
23
When given a position function, you can find the acceleration function by...
taking second derivative
taking first derivative
none
integrating
24
Where can absolute max/min values occur?
at endpoints
at critical values
none of the above
both of the above
25
If dy/dt = ky, then y = ???
Cet
ky
ekt + C
Cekt
26
d/dx[ f(g(x))] =
f'(g(x))∙g'(x)
f'(g(x))
f'(g'(x))
f'(x)∙g'(x)
27
When you see Limits at Infinity, your answer will be....
0 if the fraction is BOTTOM heavy
all the above
ratio of coefficients if num degree EQUAL to dem degree
DNE if the fraction is TOP heavy
28
Quotient Rule for f(x)/g(x) is...
[ gf' - fg' ] / g2
f'/g'
gf' + fg'
[ gf' + fg' ] / g2
29
When given a velocity function, you can find the position function by...
none
taking second derivative
integrating
taking one derivatives
30
A Left-Riemann sum is an overestimate if..
f(x) = 0
f(x) is increasing
f(x) is constant
f(x) is decreasing

Duplicate of Calculus AP Review Flashcards | StudBud

Duplicate of Calculus AP Review

30 termsStudBud Administration14 plays

calculus term review

Flashcards30 cardsFPractice quizPHost liveL

Questions 30

Answers

1
You can differentiate at a point c if...
there is a cusp at c
there is a jump at c
the limit of f'(c) is the same from both sides
there is a vertical tangent at c
2
When finding volume perpendicular to the y-axis, your bounds & equations must in terms of...
x
huh?
z
y
3
What does this represent?
average velocity
blah
average acceleration
average position
4
Derivative of xⁿ is
xn+1/(n+1)
nxn-1
xn
nxn+1
5
You have a horizontal tangent line if...
dy/dx = 0
d2x/dy2 = 0
f(x) = 0
x = 0
6
This equals.... ???
f(g(x))
f(g(x))∙g'(x)
f(x) + C
f(t)
7
d/dx of x^1/2 is...
1/(2x)
(-1/2)x
1/2
1/(2x1/2)
8
A function is continuous at a 'c' if...
f(c) is defined
f(c) = limit as x approaches c
limit as x approaches c exisits
all the above
9
What does this represent?
average position
blah
average velocity
average acceleration
10
What does this represent?
total distance
0
acceleration
displacement
11
What does this represent?
displacement
acceleration
0
total distance
12
How do you find area between curves
both
none
∫(right - left)dy
∫(top - bottom)dx
13
How do you separate variables to find solutions?
integrate
derive
add or subtract
divide or multiply
14
What does this formula find??
slope
average rate of change
integral
average value of a function
15
You have a relative max when...
f(x) changes from positive to negative
f'(x) = 0
f'(x) change from postive to negative
f"(x) changes from postive to negative
16
You have a point of inflection when...
f"(x) = 0 & f"(x) changes sign
none of the above
f"(x) = 0 & slope of f'(x) changes sign
both of above
17
When you see "average rate of change on [a, b]" you should think...
all of the above
[ f(b) - f(a) ] / (b - a)
slope of the secant line
algebra slope
18
Derivative of 1/x
-1/x2
1/x2
x0/0
ln(x)
19
Particle is speeding up because...
v > 0 & a > 0
both of the above
none of the above
v < 0 & a < 0
20
What are you being asked to find?
integral
find 0's
derivative
limit
21
Instantaneous Rate of Change of f at a:
calculus slope
all of the above
slope of tangent line
f'(a)
22
Product Rule for f(x)g(x) is...
gf' - fg'
gf' + fg'
f'∙g'
multiplication
23
When given a position function, you can find the acceleration function by...
taking second derivative
taking first derivative
none
integrating
24
Where can absolute max/min values occur?
at endpoints
at critical values
none of the above
both of the above
25
If dy/dt = ky, then y = ???
Cet
ky
ekt + C
Cekt
26
d/dx[ f(g(x))] =
f'(g(x))∙g'(x)
f'(g(x))
f'(g'(x))
f'(x)∙g'(x)
27
When you see Limits at Infinity, your answer will be....
0 if the fraction is BOTTOM heavy
all the above
ratio of coefficients if num degree EQUAL to dem degree
DNE if the fraction is TOP heavy
28
Quotient Rule for f(x)/g(x) is...
[ gf' - fg' ] / g2
f'/g'
gf' + fg'
[ gf' + fg' ] / g2
29
When given a velocity function, you can find the position function by...
none
taking second derivative
integrating
taking one derivatives
30
A Left-Riemann sum is an overestimate if..
f(x) = 0
f(x) is increasing
f(x) is constant
f(x) is decreasing