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1. the slope of a tangent to a curve 2. the slope of a tangent to a curve yy f x x 3. the slope of a tangent to a curveyy f xpx k 4. the slope of a

1. the slope of a tangent to a curve 2. the slope of a tangent to a curvey y f xx 3. the slope of a tangent to a curve y y f x px k 4. the slope of

1. concavity 2. concavity the second deriviative measures the change in slope with respect to x, this is known as concavity 3. concavity the second deriviative measures the

the primitive function the primitive function if we know the equation of the tangent, how do we find the original curve? the primitive function c n xxf xxf

1. geometrical applications of differentiationthe first derivative 2. geometrical applications of differentiationddythe first derivative y, f x , f x

1. critical points 2. critical pointsdy critical points occur when= 0 or is undefineddx 3. critical pointsdy critical points occur when= 0 or is undefineddx yx 4. critical

1. the second derivative 2. the second derivatived2 d2yy, f ( x ) , 2 { f ( x )} , 2dx dx 3. the second derivatived2 d2yy, f ( x ) , 2 { f ( x )}

1. differentiability 2. differentiability a function is differentiable at a point if the curve is smooth continuous i.e. lim f x lim f x

1. calculus rules 2. calculus rules1. chain rule d ndx u nu n1 u 3. calculus rules1. chain rule d ndx u nu n1 u bring down

limits & continuity limits & continuity a limit describes the behaviour of functions. limits & continuity a limit describes the behaviour of functions. lim

rates of change e.g. a block of ice in the form of a cube has one edge 10 cm long. it is melting so that its dimensions decrease at the rate of 1 mm/s. at what rate is the

1. rules for differentiation 2. rules for differentiation (1) y c 3. rules for differentiation (1) y c f x c 4. rules for differentiation (1) y c f

1. calculus rules 2. calculus rules d 2. product rule uv uv vu dx 3. calculus rules d 2. product rule uv uv vu dx write down

1. differentiability 2. differentiabilitya function is differentiable at a point if the curve is smooth continuous i.e. lim f x lim f x

calculus rules calculus rules 3. quotient rule 2 d u vu uv dx v v calculus rules 3. quotient rule square the bottom, write down the

1. rules for differentiation 2. rules for differentiation(1) y c 3. rules for differentiation(1) y cf x c 4. rules for differentiation(1) y cf

1. limits & continuity 2. limits & continuity a limit describes the behaviour of functions. 3. limits & continuity a limit describes the behaviour of functions.

calculus rules calculus rules 3. quotient rule 2 d u vu uv dx v v calculus rules 3. quotient rule square the bottom, write down the

1. the slope of a tangent to a curve 2. the slope of a tangent to a curve yy f x x 3. the slope of a tangent to a curveyy f xpx k 4. the slope of a

locus locus the collection of all points whose location is determined by some stated law. locus locus the collection of all points whose location is determined by some stated