13/14/15 - differentiation/ integration Flashcards

1
Q

gradient is the

A

rate of change of x with respect to y

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2
Q

differentiation notation

A

dy/dx
f’(x)

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3
Q

differentiation

A

y= ax^n
dy / dx = anx ^n-1
times by the power of x then -1 from the power
eg y = x^3
dy / dx = 3x^2

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4
Q

second order derivative

A

differentiate twice
f’‘(x)
d^2y/ dx^2
rate of change of the gradient of a function

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5
Q

summing functions

A

is y = f(x) + g(x)
dy/ dx = f’(x) + g’(x)

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6
Q

a function is increasing if

A

dy/dx >0
and decreasing if its <0

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7
Q

a point is a max / min if

A

max if f’‘(x) <0
min if f’‘(x) >0
if second order deriveative = 0 could be max/ min or inflection point

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8
Q

integration

A

S y= ax^n
dx = a/(n+1) x ^n+1 + c
add one to the power and divide by new power

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9
Q

integration notation

A

S (equation) dx = (integrated form) +c
if definite write in [ ] with limits outside

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10
Q
A
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