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KCET2019MathematicsApplication of Derivatives

The interval in which the function ( f(x)=x³-6 x²+9 x+10 ) is increasing in

Options

  1. A((- , 1] [3, ) )
  2. B((- ,-1] [3, ) )
  3. C( (- , 1) (3, ) )
  4. D( [1,3] )

Correct answer

A. ((- , 1] [3, ) )

Step-by-step solution

( aligned &f(x)=x³-6 x²+9 x+10 &f^ (x)=3 x²-12 x+9 &f^ (x)=3 (x²-4 x+3 ) &f^ (x)=3(x-1)(x-3) aligned ) For (f(x) ) to be inereasing, we must have ( aligned & F^ (x) > 0 & 3(x-1)(x-3) > 0 &(x-1)(x-3) > 0 & x 3 & x (- , 1) (3, ) & SO, F(x) is increasing on x (- , 1) (3, ) . aligned ) For (f(x) ) to be decrecsing, we must hare (F^ (x)

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