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Home / Doubts and Solutions/JEE/Mathematics

The maximum & minimum values of the function y=x^3-3x^2+6

1)2,0     2)6,0     3)6,2     4)4,2

Asked by anam.asfia99 25th October 2018, 5:24 PM
Answered by Expert
Answer:
y equals x cubed minus 3 x squared plus 6 d i f f e r e n t i a t e space w. r. t space x fraction numerator d y over denominator d x end fraction equals 3 x squared minus 6 x n o w space e q u a t e space fraction numerator d y over denominator d x end fraction equals 0 h e n c e space 3 x squared minus 6 x equals 0 3 x left parenthesis x minus 2 right parenthesis equals 0 x equals 0 space o r space x equals 2 fraction numerator d y over denominator d x end fraction equals 3 x squared minus 6 x a g a i n space d i f f e r e n t i a t e space w. r. t space x space w e space g e t fraction numerator d squared y over denominator d x squared end fraction equals 6 x minus 6 n o w space a t space 0 comma space space fraction numerator d squared y over denominator d x squared end fraction less than 0 space a n d space a t space 2 space fraction numerator d squared y over denominator d x squared end fraction greater than 0 h e n c e space f u n c t i o n space i s space m a x i m u m space a t space 0 space a n d space m i n i m u m space a t space 2 i f space w e space s u b s t i t u t e space 0 space a n d space 2 space i n space y equals x cubed minus 3 x squared plus 6 w e space g e t space 6 space a n d space 2 h e n c e space m a x i m u m space v a l u e space i s space 6 space a n d space m i n i m u m space v a l u e space i s space 2 A n w e r space i s space O P T I O N space C
Answered by Expert 29th October 2018, 4:22 PM
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