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33 Cards in this Set
- Front
- Back
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a straight line that touches the curve without crossing it
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Tangent
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another function that gives the gradient of y=f(x) at any point in the x domain
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derivative
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when the curve is increasing the gradient is ______
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positive
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when the curve is decreasing the gradient is_____
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negative
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the gradient at a stationary point is _______
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zero
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the gradient at a turning point is _______
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zero
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when the gradient is zero the tangent is ______
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horizontal
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the line segment between two intersection points
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chord
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f'(x) is the ______ of f(x)
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derivative
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the process of finding the derivative
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differentiation
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the process of finding lim(h-->0) of the gradient of the chord
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differentiation from first pricinples
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the formula for the differentiation from first principles
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f'(X)= lim(h-->0) (f(x+h)- f(x))/ h
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when we differentiate kf(x) where k is constant we get _____
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kf'(x)
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if y= x^n then dy/dx= _______
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nx^(n-1)
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lines which pass through the graph and are perpencdicular to the tangent
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normal
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the function increases (as x gets larger so does y) when dy/dx is ______
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positive
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the function decreases(as x gets larger y gets smaller) when dy/dx is ______
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negative
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the term meaning the graph is curving upwards
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concave up
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the term meaning the graph is curving downwards
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concave down
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d/dx (sinx) =
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cosx
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d/dx (cosx) =
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-sinx
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d/dx (tanx) =
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sec^2 x
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d/dx (e^x)
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e^x
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d/dx(lnx)
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1/x
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the gradient of the normal for y=f(x)
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-(1/f'(x))
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the gradient of the tangent for y=f(x)
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f'(x)
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when a point of a maximum or minimum the gradient is _____
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zero
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if (d^2 y / d^2 x )< 0 at a stationary point then this point is a _______
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maximum
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if (d^2 y / d^2 x )> 0 at a stationary point then this point is a _______
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minimum
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if (d^2 y / d^2 x )= 0 at a stationary point then this point is a _______
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no conclusion (check points beside it). Could be a point of inflexion.
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stationary point where gradient on either side is either both +ve or -ve
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point of inflexion
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at a point of inflexion d^2 y / dx^2 = ____
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zero
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the third derivative being non-zero tells us that the point is a point of
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inflexion
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