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 in 0 , 1 , respectively, then the ordered pair ( k , K ) is equal to:, 2 - 0.4 , 1, 2 - 0.6 , 1, 2 - 0.4 , 2 0.6, 1,2 0.6

MARKS App · Accepted Answer

f x = 1 + x 0.6 1 + x 0.6 f ′ x = 0.6 1 + x - 0.4 1 + x 0.6 - 0.6 x 0.4 1 + x 0.6 1 + x 0.6 2 = 0.6 1 + x - 0.4 1 + x 0.6 - x - 0.4 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 , 1 ] minimum value would be at x = 1 . ( 1 + 1 ) 0.6 1 + 1 0.6 = 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

Search any question & find its solution

Looking for more such questions to practice?