## 4/5 math terms

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jphil13  on April 6, 2011

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# 4/5 math terms

 Orthogonal Curves areAt points of intersection of the curves, the tangent lines are perpendicular.
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Orthogonal Curves areAt points of intersection of the curves, the tangent lines are perpendicular.
Intermediate Value TheoremIf f(x) is continuous on [a,b] and f(a) ≠ f(b)
then
There is a "c" inside (a, b) such that f(c) = N
where N is between f(a) and f(b)
Differential dy =
f(x) is CONTINOUS at x = a if
1)
2)
3)
Instantaneous Rate of Changef ' (a)
Definition of an EVEN function
(cos x is even)
f(x) = f(-x)
If f(x) is differentiable at x = a ,
is f(x) continuous at x = a ?
Vice versa?
Yes
Not necessarily (Ex- peaks)
Definition of an ODD function
(sin x is odd)
f(-x) = - f(x)
Rate of Change formula on [a,b]
SLOPE
limit that represents the
DEFINITION of the DERIVATIVE
Extreme Value Theorem
(where could absolute extrema occur?)
f is continuous on [a,b]

f will have an absolute max and min at either
the endoints or at the critical points
Growth and Decay Formula
"the rate at which population grows
is proportional to the original
amount (or amount present)"
Logistic Equation
dP/dt =
Mean Value Theorem
given velocity, want to find s(a). You are given s(b).
How do you find displacement of a particle between time a and b.
Area under velocity curve gives displacement.
Speed increases:

Speed decreases:
Speed increases: velocity and acceleration have same signs

Speed decreases: velocity and acceleration have different signs
particle changes direction whenvelocity changes sign
s(t) = position function
s ' (t) =
s " (t) =
s ' (t) = velocity
s " (t) = acceleration
Total Distance Traveled
Particle moves:
Left/down when __________
Right/up when __________
(left/down) velocity < 0
(right/up) velocity > 0
Particle is stopped whenv(t) = 0

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