IB Mathematics HL SL-Maxima and Minima

In my previous post, we discussed how to find the equation of tangents and normal to a curve. There are a few more  Applications of Derivatives in IB Mathematics HL SL, ‘Maxima and Minima’ is one of them.

Maxima and Minima:-

1. A function f(x) is said to have a maximum at x = a if f(a) is greater than every other value assumed by f(x) in the immediate neighbourhood of x = a. Symbolically

 

\left. \begin{array}{l} f(a) > f(a + h)\\ f(a) > f(a - h) \end{array} \right] \Rightarrow x = a   gives maxima for a sufficiently small positive h.

Similarly, a function f(x) is said to have a minimum value at x = b if f(b) is least than every other value assumed by f(x) in the immediate neighbourhood at x = b. Symbolically

 

\left. \begin{array}{l} f(b) > f(b + h)\\ f(b) > f(b - h) \end{array} \right]  If x = b gives minima for a sufficiently small positive h.

 

<img src="IB Mathematics HL SL.jpg" alt="IB Mathematics HL SL">

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