COMEDK2022MathematicsApplication of Derivatives

Let f(x)=a-(x-3)^ 8 / 9 , then maxima of f(x) is

Options

A3
Ba-3
Ca
DNone

Correct answer

C. a

Step-by-step solution

(x-3)^ 8/9 = ((x-3)^ 1/9 )^8 0 for all real x , with minimum value 0 at x = 3 . Therefore f(x) = a - (x-3)^ 8/9 a , with maximum value a at x = 3 . Alternatively, f'(x) = - 8 9 (x-3)^ -1/9 , which is undefined at x = 3 . For x 0 (increasing) and for x > 3 , f'(x) Maximum value = f(3) = a .

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