Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals: (iii) f (x) = 4x-1/2x^2, x∈[-2,9/2] (iv) f(x)=(x-1)^2+3, x∈[-3,1]
Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals: (iii) f (x) = 4x-1/2x^2, x∈[-2,9/2] (iv) f(x)=(x-1)^2+3, x∈[-3,1]

(iii) Given:  

 

Now 

 

  

At  

At  

At  

Therefore, absolute minimum value is  and absolute maximum value is 8.

(iv) Given:  

 

Now 

 

 

At  

At  

Therefore, absolute minimum value is  and absolute maximum value is 19.