COMEDK2024MathematicsApplication of Derivatives

Let f(x)=5+(2 x-3)^ 4 3 , then the minimum value of f(x) is

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Correct answer

A. 5

Step-by-step solution

We have, f(x)=5+(2 x-3)^ 4 3 Differentiate w.r.t. x aligned f^ (x) & =0+ 4 3 (2 x-3)^ 1 3 2 f^ (x) & = 8 3 (2 x-3)^ 1 3 f^ (x) & = 8 3 (2 x-3)^ 1 3 =0 2 x-3 & =0 x & = 3 2 aligned Hence, aligned & f ( 3 2 )=5+ (2 ( 3 2 )-3 )^ 4 3 & f ( 3 2 )=5 aligned

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