MHT CET202123 Sep 2021Evening ShiftMathematicsApplication of DerivativesActual

If x=-2 and x=4 are the extreme points of y=x^3- x^2- x+5 , then

Options

A=3, =24
B=-24m =-3
C=-3, =-24
D=24 , =3

Correct answer

A. =3, =24

Step-by-step solution

aligned & y=x^3- x^2- x+5 & d y d x =3 x^2-2 x- aligned We have x =-2 and x =4 as extreme points. aligned & ( d y d x )_ x=-2 =3(-2)^2-2 (-2)- =0 & 12+4 - =0 4 - =-12 & ( d y d x )_ x=4 =3(4)^2-2 (4)- =0 & 48-8 - =0 8 + =48 aligned Solving eq. (1) and (2), we get =3, =24

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