Differentiation Flashcards

1
Q

What do these terms represent?
Rate of change, gradient function and derived function

A

Differentiation

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2
Q

How do you find the gradient of a tangent to a curve?

A

Differentiate the substitute x to find the gradient

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3
Q

How do you find the equation of the tangent to a curve?

A
  • Differentiate and sub in x to find gradient
  • find y by substituting x into original equation
  • use y-b=m(x-a)
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4
Q

How do you sketch a graph of the derivative?

A
  • f ’(x) = 0 at st. pts. To find roots
  • find shape of graph using gradient
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5
Q

A function is increasing when…

A

f ’(x) > 0

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6
Q

A function is decreasing when…

A

f ’(x) < 0

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7
Q

A function is stationary when…

A

f ‘(x) = 0

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8
Q

How do you find stationary points of a function?

A

At stationary points f ‘(x) = 0
Differentiate and solve to find x values
Substitute back in to find y values
Use a nature table to determine the nature

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9
Q

How do you find where a function is increasing or decreasing?

A

Differentiate then use a nature table (or solve the inequality)

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10
Q

How do you show a function is ALWAYS increasing (decreasing)?

A

Differentiate then complete the square to show that f ‘(x) > 0 (f ‘(x) < 0) for all values of x

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11
Q

How do you find the solution to an optimisation problem?

A

Investigate stationary points (and end points if necessary)

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12
Q

What do you get if you differentiate distance?

A

Speed

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13
Q

What do you get if you differentiate speed?

A

Acceleration

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14
Q

What do you get if you differentiate sinx?

A

Cosx

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15
Q

What do you get if you differentiate cosx?

A
  • sinx
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16
Q

What is the chain rule for differentiation?

A

f ‘(g(x)) x g ‘(x)
(Differentiate around the brackets, then multiply by the derivative of what’s inside the brackets)

17
Q

What do you get if you differentiate sin(ax+b)?

A

acos(ax+b)

18
Q

What do you get if you differentiate cos(ax+b)

A

-asin(ax+b)