Ch.12 Differentiation Flashcards
what is the gradient of a curve at a given point defined as?
the gradient of the tangent to the curve at that point
what is the derivative?
the gradient function of the curve
how is the derivative written?
f’(x) = dy/dx = lim h>0 f(x+h) - f(x) / h
how would you differentitaite a term like x to the power of n?
multiply by power then subtract 1 from the power
what is the normal to the curve at point?
a straight line perpendicular to the tangent at point A
how would you know if a curve is increasing?
if the gradient is greater than or equal to 0 ( if its positive )
how would you know if a curve is decreasing?
if the gradient is lesser than or equal to 0 ( if its negative )
what is a stationary point?
any point on the curve where f’(x) = 0
what is a local maximum stationary point?
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
what is a local minimum stationary point?
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
what is a point of inflection?
stationary point that has a gradient change of positive to 0 to positive or negative to 0 to negative