Definition of Derivative (Chapter 2)
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| Definition: The Intermediate Value Theorem (IVT) | show 🗑
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| Definition: Average Rate of Change | show 🗑
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| show | sin (x + h) = sin(x)cos(h) + sin(h)cos(x)
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| Sum formula for cosine | show 🗑
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| show | "Global Derivative"
Lim h–>0 [ f (x+h) – f(x) ] / h
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| What does it mean to take the derivative of a function? | show 🗑
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| show | Displacement or Position Function: s(t),
Velocity: s '(t) = v(t),
Acceleration: s '' (t) = v ' (t) = a(t).
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| show | 1) Must be in "Ax + By = C" form
2) where A, B, & C are integers
3) and "A" must be a positive value
m = –A / B or first number over the second and "change the sign".
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| show | Slope - y–intercept: y = mx + b or y = (∆y / ∆x) x + b.
Standard: Ax + By = C
Point–Slope: (y–k) = m (x–h)
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| show | "Disposable Derivative".
Lim x–>c [ f (x) – f(c) ] / (x – c)
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| show | States that if a function f is continuous on the closed interval [a,b], and differentiable on the open interval (a,b),
then there exists at least point c in the interval (a,b) such that
f'(c) is equal to the average rate of change over [a,b].
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| Average VS Instantaneous Rates of Change | show 🗑
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| Estimating the Instantaneous Rate of Change | show 🗑
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| show | When being asked about instantaneous velocity, this is a translation for instantaneous rate of change of displacement. S'(t) = v(t).
This is a direct substitution into the velocity function. DO NOT MOVE a level!
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| show | When being asked about instantaneous acceleration, this is a translation for instantaneous rate of change of velocity. S''(t) = v'(t) = a(t).
This is a direct substitution into the acceleration function.
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| Understanding the terminology for "Instantaneous rate of change" | show 🗑
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| Understanding the terminology for "Average velocity" | show 🗑
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| Understanding the terminology for "Average acceleration" | show 🗑
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| Understanding the terminology for "Average rate of change" | show 🗑
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| show | From the perspective of displacement S(t), max/min is found when S'(t) = v(t) = 0. One MUST MOVE DOWN a level and set equal to zero.
Ex. Any function h''(x), One MUST MOVE DOWN a level and set equal to zero. So h'''(x)=0
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Created by:
Troy.Criswell
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