JEE Main & Advanced Mathematics Applications of Derivatives Question Bank

done Numerical Value Type Questions - Maxima and Minima Total Questions - 10

• question_answer1)
  The tangent to the curve \[y={{x}^{3}}-6{{x}^{2}}+9x+4,0\le x\le 5\] has maximum slope at \[x=k\] then find value of k.
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• question_answer2)
  If the function \[f\left( x \right)=2{{x}^{3}}-9a{{x}^{2}}+12{{a}^{2}}x+1\] where \[a>0,\] attains its maximum and minimum at p and q respectively such that \[{{p}^{2}}=q\], then find a.
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• question_answer3)
  Find the smallest value of the polynomial \[{{x}^{3}}-18{{x}^{2}}+96x\] in the interval \[\left[ 0,9 \right].\]
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• question_answer4)
  The minimum value of \[ax+by,\] where \[xy={{r}^{2}},\left( r,ab>0 \right)\] is \[\lambda r\sqrt{ab}\] then find \[\lambda \].
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• question_answer5)
  Find the minimum value of the function \[f\left( x \right)=2\,\,\left| x-2 \right|+5\,\,\left| x-3 \right|\]for all \[x\in R.\]
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• question_answer6)
  If \[y=a\,\,\log \,\,\left| x \right|+b{{x}^{2}}+x\] has its extremum values at \[x=-1\] and \[x\text{ }=\text{ }2\] then find value of \[a\text{ }+\text{ }b.\]
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• question_answer7)
  If \[ab=2a+3b,a>0,b>0,\]then find the minimum value of ab.
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• question_answer8)
  Using wire of length 20 m, boundary of a garden which is in the shape of a circular sector is made. If Area of the garden is maximum, then find the radius of the sector.
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• question_answer9)
  If maximum value of \[\frac{1}{{{x}^{2}}-3x+6}\] is \[\frac{a}{b}\]then find value of a + b.
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• question_answer10)
  Difference between the greatest and the least values of the function \[f\left( x \right)=x\left( \ell n\,x-2 \right)\] on \[\left[ 1,{{e}^{2}} \right]\] is \[\lambda {{e}^{k}}\] then find \[\lambda +k\].
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