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Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

Let f(x) be double differentiable function such that |f^ (x) | 5 x [0,4] and f takes its largest value at an interior point of this interval. Then the value of |f^ (0) |+ |f^ (4) | can be:

Options

  1. A18
  2. B19
  3. C20
  4. D21

Correct answer

C. 20

Step-by-step solution

Since, f attains its maximum value at some c (0,4) f^ (c)=0 Now, in y=f^ (x) using LMVT in [0, c] and [c, 4] |f^ (d) |= | f^ (c)-f^ (0) c | 5 |f^ (0) | 5 c ....(1) Again, |f^ (d) |= | f^ (4)-f^ (c) 4-c | 5 |f^ (4) | 5(4-c) ...(2) Eqn. (1) + eqn. (2) |f^ (0) |+ |f^ (4) | 20 .

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