Ch.12 Differentiation Flashcards

1
Q

what is the gradient of a curve at a given point defined as?

A

the gradient of the tangent to the curve at that point

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2
Q

what is the derivative?

A

the gradient function of the curve

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3
Q

how is the derivative written?

A

f’(x) = dy/dx = lim h>0 f(x+h) - f(x) / h

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4
Q

how would you differentitaite a term like x to the power of n?

A

multiply by power then subtract 1 from the power

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5
Q

what is the normal to the curve at point?

A

a straight line perpendicular to the tangent at point A

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6
Q

how would you know if a curve is increasing?

A

if the gradient is greater than or equal to 0 ( if its positive )

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7
Q

how would you know if a curve is decreasing?

A

if the gradient is lesser than or equal to 0 ( if its negative )

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8
Q

what is a stationary point?

A

any point on the curve where f’(x) = 0

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9
Q

what is a local maximum stationary point?

A

shaped like a “n” and has a gradient change from positive to 0 to negative

  • second order derivative will be less than or equal to 0
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10
Q

what is a local minimum stationary point?

A

shaped like a “u” and has a gradient change from negative to 0 to positive

  • second order derivative will be greater than or equal to 0
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11
Q

what is a point of inflection?

A

stationary point that has a gradient change of positive to 0 to positive or negative to 0 to negative

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