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AP EAMCET202419 May 2024Evening ShiftMathematicsFunctionsActual

For all x [0,2024] assume that f(x) is differentiable, f(0)=-2 and f^ (x) 5 . Then the least possible value of f (2024) is

Options

  1. A10120
  2. B10118
  3. C10122
  4. D10116

Correct answer

B. 10118

Step-by-step solution

Given d(f(x)) d x 5 aligned & d(f(x)) 5 d x f(x) 5 x+c & f(0) 0+c -2 c So, c=(- ,-2] aligned Now f(2024) 5 2024+c=10120+c For least value of f(2024) , we take c=-2 So, f(2024)=10120-2 (which is least) Least value of f(2024)=10118

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