Differentiation Flashcards
at any point on a curve what is the normal line
the line that goes through the point and is perpendicular to the tangent
what are the two equation forms of a straight line
y = mx + c
y - y1 = m(x - x1)
when is a function decreasing and what does this mean
when the gradient is negative
this means the gradient goes down as x increases
opposite for an increasing function
how to find out the intervals (range of x values) for which a curve is increasing or decreasing
what notation would you use for the second derivative
what is the second derivative (in words)
the FIRST derivative is the rate of change of a function
the SECOND derivative is the rate of change of the rate of change ie. the rate of change of the gradient
a positive second derivative means:
the gradient is increasing (graph is becoming steeper)
eg a u shape where the gradient is changing from negative to positive
a negative second derivative means
the gradient is decreasing (graph becoming less steep)
eg an n shape where the gradient is changing from positive to negative
if f(x) is the function then what is the gradient function notation
f’(x)
what is the notation for the second derivative when the function is f(x)
f’‘(x)
how to figure out whether a turning point of a graph is a local maximum, a local minimum or a point of inflection
what is the normal line of a graph
the line perpendicular to the tangent at any point
how to find the minimum or maximum value of a curve
the y coordinate
