Consider f(x)=a x^3-b x^2+c x+d , where a = ⁻¹( 4)+ 2 aligned & b = 3 ( cosec ⁻¹ cosec 6+2 ) 2 & c = ( ⁻¹ 10 )+3 +2 & ~d =5 (2 - ⁻¹ 5 ) aligned If p represents the number of extremum of the function f( x ) and q represents the number of rea

Question

Consider f(x)=a x^3-b x^2+c x+d , where a = ⁻¹( 4)+ 2 aligned & b = 3 ( cosec ⁻¹ cosec 6+2 ) 2 & c = ( ⁻¹ 10 )+3 +2 & ~d =5 (2 - ⁻¹ 5 ) aligned If p represents the number of extremum of the function f( x ) and q represents the number of real roots of the equation f( x )=0 , then find the value of p + q .

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Correct answer: 3

aligned & a = 4- + 2 =2 & ~b = 3(6-2 +2 ) 2 =9 & c =10-3 +3 +2=12 & ~d =5 2 -(2 -5) =25 & f( x )=2 x ^3-9 x ^2+12 x +25 aligned f^ (x)=6(x-2)(x-1) from graph aligned & p =2 & q =1 aligned

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