Flashcards
AP Calculus Must Know Concepts
Flashcards do conjunto (83)
- 1—a/b
- 2—1
- 3—0
- 4—1
- 5—a/b
- 6—1
- 7—0
- 8The # that makes only the denominator = 0 is called a ______vertical asymptote
- 9A ____ occurs at the points that the numerator and the denominator = 0 at the same timehole
- 10A function f is continuous at x=c if...
- 11Equation of a line (point-slope form)y - y1 = m(x - x1)
- 12—f(x) = sin x
f'(x) = cos x
- 13—f(x) = sin x
f'(x) = cos x
f'(π/2) = 0
- 14Alternative definition of a derivative
- 15—
- 16—f'(x)*g(x) + f(x)*g'(x)
- 17—
- 18—
- 19—cos x
- 20—-sin x
- 21—
- 22—-csc(x)cot(x)
- 23—sec(x)tan(x)
- 24—
- 25—
- 26—
- 27—
- 28—
- 29—
- 30—
- 31Volume of a sphere
- 32Surface area of a sphere
- 33Area of a circle
- 34Circumference of a circle
- 35Volume of a cylinder
- 36Volume of a cone
- 37The first derivative can be used to find...max. and min., increasing and decreasing, slope of the tangent line to the curve, and velocity.
- 38The second derivative can be used to find...inflection points, concavity, and acceleration
- 39f(x) is increasing when...f'(x) > 0
- 40f(x) is decreasing when...f'(x) < 0
- 41f(x) has a relative maximum when...f'(x) changes from positive to negative
- 42f(x) has a relative minimum when...f'(x) changes from negative to positive
- 43f(x) has a point of inflection when...f''(x) switches signs or f'(x) switches from increasing <-> decreasing
- 44f(x) is concave up when...f''(x) > 0 or f'(x) is increasing
- 45f(x) is concave down...f''(x) < 0 or f'(x) is decreasing
- 46Critical values occur when the first derivative is...equal to zero or undefined
- 47—ax+C
- 48—
- 49—
- 50—
- 51—-cos x + C
- 52—sin x + C
- 53—
- 54—
- 55—
- 56—
- 57—tan x + C
- 58—-cot x + C
- 59—sec x + C
- 60—-csc x + C
- 61—ln|x|+C
- 62—
- 63—
- 64—
- 65Given a position function, its derivative is the ____ function.velocity
- 66Given a velocity function, its derivative is the ____ functionacceleration
- 67Given s(t) as the position function, the formula for AVERAGE VELOCITY in the interval (a,b) is _________
- 68Given v(t) as the velocity function, the formula for AVERAGE ACELERATION in the interval (a,b) is ________
- 69A particle is moving to the right or up whenv(t) > 0
- 70A particle's position is increasing whenvelocity is positive
- 71A particle is moving to the left or down whenv(t) < 0
- 72A particle's position is decreasing whenvelocity is negative
- 73A particle is at rest or changing direction whenv(t)=0
- 74A particle is speeding up (speed is increasing) if its...velocity and acceleration have the same sign at that point
- 75A particle is slowing down (speed is decreasing) if its...velocity and acceleration have opposite signs at that point
- 76A particle is moving towards the origin when its position and velocity have...the opposite signs
- 77A particle is moving away from the origin when its position and velocity have...the same signs
- 78Displacement is the...change in positions between two times. Displacement can be negative
- 79Total distance travelled is...
- 80Speed is...the absolute value of velocity
- 81Mean Value Theorem
- 82Formula for the area between the curve
- 83—