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33 Cards in this Set
 Front
 Back
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^(n1)


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 nonzero tells us that the point is a point of

inflexion
