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It is given that at x = 2, the function x3 - 12x2 + kx - 8 attains its maximum value, on the interval [0, 3]. Find the value of k
1. 23
2. 34
3. 36
4. 35
5. None of these

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Correct Answer - Option 3 : 36

Concept:

Following steps to finding maxima and minima using derivatives.

  • Find the derivative of the function.
  • Set the derivative equal to 0 and solve. This gives the values of the maximum and minimum points.
  • Now we have to find the second derivative.
  1. f``(x) is less than 0 then the given function is said to be maxima
  2. If f``(x) Is greater than 0 then the function is said to be minima


Calculation:

Let f(x) = x3 - 12x2 + kx – 8

Differentiating with respect to x, we get

⇒ f’(x) = 3x2 – 24x + k

It is given that function attains its maximum value of the interval [0, 3] at x = 2

∴ f’(2) = 0

⇒ 3 × 22 – (24 × 2) + k = 0

∴ k = 36

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