What is maxima, minima or inflexion in a graph ?
Answer :
Let f be a function defined on an interval [a,b] or (a,b), and let p be a point in (a,b), i.e.,
not an endpoint, if the interval is closed.
• f has a local minimum at p if f(p) ≤ f(x) for all x in a small interval around p.
• f has a local maximum at p if f(p) ≥ f(x) for all x in a small interval around p.
• f has an inflexion point at p if the concavity of f changes at p, i.e. if f is concave down on one side of p and concave up on another.
So we can show maxima and minima on graph , As :
Here A is Maxima And B is Minima
And
All points at which f(x) = 0 are called stationary points but as shown in the sketch below there are stationary points which are neither local maxima nor local minima..
P is in fact an example of a type of point known as a point of inflexion .
Let f be a function defined on an interval [a,b] or (a,b), and let p be a point in (a,b), i.e.,
not an endpoint, if the interval is closed.
• f has a local minimum at p if f(p) ≤ f(x) for all x in a small interval around p.
• f has a local maximum at p if f(p) ≥ f(x) for all x in a small interval around p.
• f has an inflexion point at p if the concavity of f changes at p, i.e. if f is concave down on one side of p and concave up on another.
So we can show maxima and minima on graph , As :
Here A is Maxima And B is Minima
And
All points at which f(x) = 0 are called stationary points but as shown in the sketch below there are stationary points which are neither local maxima nor local minima..
P is in fact an example of a type of point known as a point of inflexion .