PYQSidePowered byPrepblink ExamsMy practice

Application of Derivatives

JEE Main 2024 (Online) 29th January Morning ShiftMCQMedium📈 Topic in 24% papers+4−1
Ques. 1JEE Main 2024, 29 January (Morning Shift)

Consider the function f: [ 12,1 ] R defined by f(x)=4 2x3-3 2x-1. Consider the statements (I) The curve y=f(x) intersects the x-axis exactly at one point. (II) The curve y=f(x) intersects the x-axis at x= 12. Then

  1. Both (I) and (II) are correct.
  2. Only (I) is correct.
  3. Both (I) and (II) are incorrect.
  4. Only (II) is correct.

Answer

(1) Both (I) and (II) are correct.

Solution

f'(x)=12 2x2-3 2=3 2(4x2-1) 0 on [ 12,1 ] ⇒ f is increasing

f ( 12 )= 22- 3 22-1=- 2-1<0, f(1)= 2-1>0

⇒ exactly one zero in [ 12,1 ] ⇒ (I) is correct

Put x= , [0, 3 ]: f(x)= 2 (4 3 -3 )-1= 2 3 -1

f(x)=0 3 = 1 2, with 3 [0, ]

3 = 4 = 12

⇒ the zero is x= 12 ⇒ (II) is correct

Answer: (1)

Keep practising — Application of Derivatives

Ques. 2JEE Main 2024, 29 January (Morning Shift)

Let f(x)=2x-x2,x R. If m and n are respectively the number of points at which the curves y=f(x) and y=f'(x) intersect the x-axis, then the value of m+n is .

Ques. 3JEE Main 2024, 29 January (Evening Shift)

The function f(x)= xx2-6x-16, x R-\-2,8\

  1. decreases in (- ,-2) (-2,8) (8, )
  2. increases in (- ,-2) (-2,8) (8, )
  3. decreases in (-2,8) and increases in (- ,-2) (8, )
  4. decreases in (- ,-2) and increases in (8, )
Ques. 4JEE Main 2024, 29 January (Evening Shift)

The function f(x)=2x+3(x) 23, x R, has

  1. exactly one point of local minima and no point of local maxima
  2. exactly one point of local maxima and exactly one point of local minima
  3. exactly two points of local maxima and exactly one point of local minima
  4. exactly one point of local maxima and no point of local minima
Ques. 5JEE Main 2024, 27 January (Evening Shift)

Let g(x)=3f ( x3 )+f(3-x) and f''(x)>0 for all x (0,3). If g is decreasing in (0, ) and increasing in ( ,3), then 8 is :

  1. 0
  2. 24
  3. 18
  4. 20

All Application of Derivatives PYQs →

PDFDownload Application of Derivatives PYQs as PDF Free, with answer key and a QR code to every solution — print it or study offline⬇
All JEE Main Mathematics chapters
Class 11SetsRelations and FunctionsTrigonometric FunctionsComplex Numbers and Quadratic EquationsPermutations and CombinationsBinomial TheoremSequences and SeriesStraight LinesConic SectionsIntroduction to Three Dimensional GeometryLimits and DerivativesStatisticsProbability
Class 12Relations and Functions (Class 12)Inverse Trigonometric FunctionsMatricesDeterminantsContinuity and DifferentiabilityApplication of DerivativesIntegralsApplication of IntegralsDifferential EquationsVector AlgebraThree Dimensional GeometryProbability (Class 12)