Rules
What is the quotient rule
Lo-di hi minus hi-di low over the square below
The function is not differntable if…
It’s not continuous, has a cusp, corner, jump, or the left and right limit of f’(x) aren’t the same.
What is the derivative of cos x
-sin x
What is ms leggio’s favorite color?
Orange
Speed in a specific direction is called
velocity
DESCRIBE THE MEAN VALUE THEOREM(MVT).
When the function is continuous on [a,b] and differentiable on (a,b) there will be at least one point where the instantaneous rate of change is equal to the average rate of change.
The function f is increasing and concave up when…
f’ >0
f”>0
What describe the instantaneous rate of change?
Slope of the tangent line
When did Leggio and McCartney start sharing a room?
School year of 2025-2026
Velocity equals speed T/F
false
DESCRIBE THE MEANING OF INTERMEDIATE VALUE THEOREM (IVT)
If the function is continuous on [a,b] there must be f(x) = c, when c is a number between f(a) and f(b).
An indefinite integral should include…
+c
When finding absolut max. Or min. In the first derivative you must…
Check the Endpoints
What concert did Leggio go in summer of 2024?
Pitbull! Fireeballll
If a particle has a positive velocity and a negative acceleration, is the particle speeding up or slowing down?
slowing down
If f has an inverse function of g then…
g’(x)= 1/(f’(g(x)))
What is the formula for a Trapezoidal Riemann Sum?
∫abf(x)dx=b-a/2n
What is the derivative of a cos-1x?
-1/(sqr(1–x2))
Who has oldest child and how old are they?
McCartney, her kid is 5
What is displacemen?
Total distance regardless of direction
Limit as x approaches 0
3x2/(ex-1-x)
6
What is the difference between a definite and indefinite integral?
A definite integral produces a specific number and the upper and lower limits are provided and an indefinite integral always include +c and no limits of integration
What is the derivative of
6xsinx + 7e2x
6sinx + cosx6x + 14e2x
When did McCartney drop calc?
Mid November of 2025
A particle moves along a line so that its position at any time 𝑡 0 is given by the function
s(t)=t3-8t2+20t-16
where s is measured in meters and t is measured in seconds.
Find the acceleration of the particle at any time t.
a(t)=6t-16