a) If the y-coordinate of the derivative function is negative over an interval, then the function is said to be over that interval. b) The is sometimes called rate of change of the slope of the tangent. at (a, f(a)). If f'(x) > 0 and f'(x) = 0 at x = a, there is a
a) If the y-coordinate of the derivative function is negative over an interval, then the function is said to be over that interval. b) The is sometimes called rate of change of the slope of the tangent. at (a, f(a)). If f'(x) > 0 and f'(x) = 0 at x = a, there is a
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:23.
b)
c)
d)
e)
f)
Calculus word bank. Fill in the blanks using the correct answer using words.
The length of the blank does not reflect the length of the answer.
concave down
maximum
endpoints
midpoint
continuous
differentiable
h)
i)
j)
negative to zero to positive
second derivative
positive to zero to negative
point of inflection
slowing down
critical numbers
first derivative
a)
If the y-coordinate of the derivative function is negative over an interval, then the
function is said to be
over that interval.
optimization
maximizing
decreasing
minimum
The
speeding up
concave up
undefined
increasing
is sometimes called rate of change of the slope of the tangent.
at (a, f(a)).
If f'(x) > 0 and f'(x) = 0 at x = a, there is a
If f'(x) changes from
x < a to x > a, then (a, f(a))is a local minimum value.
The absolute maximum can often be found at the
If h(x) = f(x)g(x), where f(x) and g(x) are
then h'(x) = f'(x) g(x) + f(x)g'(x)
as x increases from
If you are looking at the graph of f'(x) over an interval, and its slope is always
negative, then you can say that ƒ(x) is.
over that interval.
of an interval.
An object is
¸ if v(t) × a(t) <0
Values in the domain where the derivative is zero or undefined are
_functions,
is finding a "best" outcome for a situation in a problem.
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