Let k and K be the minimum and the maximum values of the function f x = 1 + x 0.6 1 + x 0.6   in   0 ,   1 , respectively, then the ordered pair ( k ,   K ) is equal to:

Question

Let k and K be the minimum and the maximum values of the function f x = 1 + x 0.6 1 + x 0.6 &#160; in &#160; 0 , &#160; 1 , respectively, then the ordered pair ( k , &#160; K ) is equal to:

Aicharya · Accepted Answer

f x = &#160; 1 + x 0.6 1 + x 0.6 f &#8242; x = &#160; 0.6 1 + x - 0.4 &#160; 1 + x 0.6 - 0.6 &#160; x 0.4 1 + x 0.6 1 + x 0.6 2 = 0.6 &#160; 1 + x - 0.4 &#160; 1 + x 0.6 - x - 0.4 &#160; 1 + x 2 1 + x 0.6 2 = 0.6 x 0.4 - 1 1 + x 0.4 1 + x 0.6 2 Clearly it is always negative in [ 0 , &#160; 1 ] minimum value would be at x = 1 . ( 1 + 1 ) 0.6 1 + 1 0.6 = &#160; 2 0.6 2 = 2 - 0.4 = k & maximum values would be at x = 0 ( 1 + 0 ) 0.6 1 + 0 0.6 = 1 1 = K Hence 2 - 0.4 , 1

Let k and K be the minimum and the maximum values of the function f x = 1 + x 0.6 1 + x 0.6   in  …

Solution

Let k and K be the minimum and the maximum values of the function f x = 1 + x 0.6 1 + x 0.6 &#160; in &#160;…

Solution

Let k and K be the minimum and the maximum values of the function f x = 1 + x 0.6 1 + x 0.6 in …