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33 Cards in this Set

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