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Home » Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be: (i) f(x) = x ^2 (ii) g(x) = x^ 3 – 3x
Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be: (i) f(x) = x ^2 (ii) g(x) = x^ 3 – 3x
Applications of Derivatives | CBSE | Class 12 | Exercise 6.5 | Maths | NCERT
Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be: (i) f(x) = x ^2 (ii) g(x) = x^ 3 – 3x

(i) Given:  

    and 

Now 

      [Turning point]

Again, when ,    [Positive]

Therefore,  is a point of local minima and local minimum value = 

(ii) Given:  

    and 

Now 

  

 

 

  or  [Turning points]

Again, when ,

 [Negative]

   is a point of local maxima and local maximum value 

And when    [Positive]

   is a point of local minima and local minimum value 

i

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