JEE Maths - Maxima & Minima

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Question - 1

The tangent to the curve y = x3 -6x2 + 9x + 4, 0 ≤ x ≤ 5 has maximum slope at x= k then find value of k _____________ .

  • A 4.00
  • B 5.00
  • C 7.00
  • D 9.00

Question - 2

If the function f(x) = 2x3 - 9ax2 + 12a2x + 1 where a > 0, attains its maximum and minimum at p and q respectively such that p2 = q, then frnd a _____________ .

  • A 0.00
  • B 1.00
  • C 2.00
  • D 3.00

Question - 3

Find the smallest value of the polynomial x3- 18x2 + 96x in the interval [0, 9] ______________ .

  • A 0.00
  • B 2.00
  • C 4.00
  • D 8.00

Question - 4

The minimum value of ax + by, where xy = r2, (r, ab > 0) is λr \( \sqrt{ab}\) then find λ _____________ .

  • A 6.00
  • B 1.00
  • C 5.00
  • D 2.00

Question - 5

Find the minimum value of the function f(x)= 2 | x-2 | + 5 | x - 3 | for all x ∈ R _____________ .

  • A 1.00
  • B 4.00
  • C 2.00
  • D 3.00

Question - 6

If y = a log | x | + bx2 + x has its extremum values at x = -1 and x = 2 then find value of a +b _____________ .

  • A 2.50
  • B 1.50
  • C 3.50
  • D 7.50

Question - 7

If ab = 2a + 3b, a > 0, b > 0, then find the minimum value of ab _____________ .

  • A 24.00
  • B 25.00
  • C 26.00
  • D 27.00

Question - 8

Using wire of length 20 m, boundary of a garden which is in the shape of a circular sector is to be made. If Area of the garden is maximum, then find the radius of the sector ______________ .

  • A 1.00
  • B 3.00
  • C 5.00
  • D 9.00

Question - 9

If maximum value of \(\frac{1}{x^{2}-3x+6}\) is \(\frac{a}{b}\) then find value of a + b _____________ .

  • A 16.00
  • B 17.00
  • C 18.00
  • D 19.00

Question - 10

Difference between the greatest and the least values of the function f(x) = x(ln x-2) on [1, e2] is λek then find λ + k ______________ .

  • A 2.00
  • B 3.00
  • C 4.00
  • D 5.00
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