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Application of Derivatives

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

Answer

(1) decreases in (- ,-2) (-2,8) (8, )

Solution

f'(x)= (x2-6x-16) 1-x(2x-6)(x2-6x-16)2

= -(x2+16)(x2-6x-16)2

∵ x2+16>0 and the denominator is a square ⇒ f'(x)<0 for every x -2,8

f decreases in each of (- ,-2),(-2,8),(8, )

Answer: (1)

Keep practising — Application of Derivatives

Ques. 2JEE 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. 3JEE 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

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