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The number of points where the function \(\;f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {{{\left( {x + 1} \right)}^4},\;\;x \le 1}\\ {{{\left( {x - 5} \right)}^2},\;\;x > 1} \end{array}} \right.\) attains its local maximum is

The number of points where the function \(\;f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {{{\left( {x + 1} \right)}^4},\;\;x \le 1}\\ {{{\left( {x - 5} \right)}^2},\;\;x > 1} \end{array}} \right.\) attains its local maximum is Correct Answer 1

Concept :

A point is said to be at local maxima when the functional value at that point is higher than the surrounding small interval.

⇒ For example, In the below graph, A is a local maximum and B can be either local maxima or global maxima depending on whether the graph has a higher value than B or not.

Mistake Points

⇒ Student often gets confused by accumulating differentiable properties and maxima and minima properties. 

⇒ In the above graph f(x) is differentiable everywhere except at O, which will not have any impact on pointing O as a local maximum.

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