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BITSAT2023MathematicsApplication of DerivativesActual

If f(x)= x, g(x)= 2 x, h(x)= 3 x and I(x)= x , then which of the following option is correct?

Options

  1. Af(x) and g(x) are strictly decreasing in (0, / 2)
  2. Bh(x) is neither increasing nor decreasing in (0, / 2)
  3. CI ( x ) is strictly increasing in (0, / 2)
  4. DAll are correct

Correct answer

D. All are correct

Step-by-step solution

(a) Let f(x)= x , then f^ (x)=- x . In interval (0, 2 ), f^ (x) Therefore, f(x) is strictly decreasing on (0, 2 ) (b) Let f(x)= 2 x f^ (x)=-2 x 2 x In interval (0, 2 ), f^ (x) Because 2 x will either lie in the first or second quadrant which will give a positive value. Therefore, f(x) is strictly decreasing on (0, 2 ) (c) Let f^ (x)= 3 x f ^ ( x )=-3 3 x . In Interval (0, 3 ), f ^ ( x ) Because 3 x will either lie in the first or second quadrant which will give a positive value. Therefore, f ( x ) irstrictly decrea

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