Login/Sign Up
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: (iii) h(x) = sin x + cos x, 0 2 x π < < (iv) f(x) = sin x – cos x, 0 2 < < π
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: (iii) h(x) = sin x + cos x, 0 2 x π < < (iv) f(x) = sin x – cos x, 0 2 < < π
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: (iii) h(x) = sin x + cos x, 0 2 x π < < (iv) f(x) = sin x – cos x, 0 2 < < π

(iii) Given:         ……….(i)

    and 

Now 

 

 

 

    [Positive]

   can have values in both I and III quadrant.

But,  therefore,  is only in I quadrant.

  =  [Turning point]

At  

  = 

=  =  =   [Negative]

   is a point of local maxima and local maximum value

= 

= 

(iv) Given:         ……….(i)

    and 

Now 

 

 

 

    [Negative]

   can have values in both II and IV quadrant.

   = 

=  or 

  or 

   and    [Turning point]

At   = 

  = 

= 

= 

=  =   [Negative]

   is a point of local maxima and local maximum value = 

= 

=  = 

At   

= 

   = 

= 

= 

=  =      [Positive]

   is a point of local maxima and local maximum value = 

= 

=  = 

i

More Material