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Manipal MET2020MathematicsApplication of Derivatives

If f(x)= aligned ( x 2 ), & if x 1 3-2 x, & if x 1 aligned . , then f(x) has

Options

  1. Alocal minimum at x=1
  2. Blocal maximum at x=1
  3. CBoth local maximum and local minimum at x=1
  4. DNone of the above

Correct answer

B. local maximum at x=1

Step-by-step solution

Given function is f(x)= array cl ( x 2 ), & if x 1 3-2 x, & if x 1 array . LHL and RHL of f(x) is 1 , when x 1 and f(1)=3-2=1 f(x) is continuous at x=1 . Now, graph of function f(x) is From the above graph of function, we see that f(x) has local maxima at x=1 .

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