Derivative Rules
Low "D" high minus high "D" low, square the bottom and you're good to go!
What is the quotient rule?
If a function is continuous on a closed interval, it must have an absolute minimum and maximum value. This theorem is...
This quantity is found by taking the absolute value of the velocity function, |v(t)|.
What is speed?
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What is UCONN?
Zero is the derivative of...
What is any constant?
By the Mean Value Theorem (MVT), if a function is continuous and differentiable on a closed interval, there must exist a point where it's (BLANK) equals it's (BLANK)
What is the INSTANTANEOUS RATE OF CHANGE and AVERAGE RATE OF CHANGE?
To find the total distance a particle travels on an interval [a, b], a student must evaluate this definite integral.
What is integral a to b v(t)dt?
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What is Ben?
This function and it's derivative are the same
What is Ex?
This theorem states that the integral of a function can be found using its antiderivative and that differentiation reverses integration
What is the Fundamental Theorem of Calculus? (FTC)
This phrase describes what is happening to a particle's speed if its velocity is positive (v(t) > 0) and its acceleration is negative (a(t) < 0).
What is slowing down? (Speed decreases when velocity and acceleration have opposite signs).
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In the inverse function rule, the derivative of (F-1)'(x) is...
What is 1/f'(f-1(x))?
Rolle's Theorem states that if a function f(x) meets the following three conditions:
f(x) is continuous on the closed interval [a, b],
f(x) is differentiable on the open interval (a, b), and
f(a) = f(b)
What is Rolle's Theorem?
When solving a differential equation with an initial condition, this mathematical step must be performed immediately after finding the antiderivative to earn full credit on an FRQ.
What is solving for the constant of integration (+C)?
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What is the Simsbury Inn?
This rule states that a constant can be pulled out of a derivative since it doesn’t affect the rate of change.
What is the constant multiple rule?
This theorem states that if a function is continuous on [a,b], it will hit every single y-value between f(a) and f(b) at least once.
What is the Intermediate Value Theorem (IVT)?
This type of discontinuity occurs at x = c if the limit as x approaches c exists, but does not equal the actual function value f(c).
What is a removable discontinuity (or a hole)?
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What is a knife block set?