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Maxima and Minima — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMaxima and Minima1 Mark
Question
The number which exceeds its square by the greatest possible quantity is,
  1. $\frac{1}{2}$
  2. $\frac{1}{4}$
  3. $\frac{3}{4}$
  4. None of these.
✓

Answer

  1. $\frac{1}{2}$

Solution:

Let the required number be x.

Then, f'(x) = x - x2

lmplies that f(x) = 1 - 2x = 0

For a local maxima or a local minima, we must have f'(x) = 0

lmplies that 2x = 1

lmplies that $\text{x}=\frac{1}{2}$

Now, f''(x) = -2 < 0

Therefore, $\text{x}=\frac{1}{2}$ is a local maxima.

Hence, the required number is $\frac{1}{2}$.

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