⭕ question No. 84 , plz explain in detail !!

Asked by vidyavikram10 | 15th Aug, 2020, 10:06: AM

Expert Answer:

f(x) = x3 - 3x2 + 6 and,
straight g left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell max space straight f left parenthesis straight x right parenthesis space semicolon space straight x plus 1 less or equal than straight t less or equal than straight x plus 2 comma space minus 3 less or equal than straight x less or equal than 0 end cell row cell 1 minus straight x space space space space space space space semicolon space straight x greater or equal than 0 end cell end table close equals open curly brackets table attributes columnalign left end attributes row cell max space straight f left parenthesis straight x right parenthesis space semicolon minus 3 less or equal than straight x less or equal than 0 end cell row cell 1 minus straight x space space space space space space space semicolon space straight x greater or equal than 0 end cell end table close
straight f apostrophe left parenthesis straight x right parenthesis equals 3 straight x squared minus 6 straight x
straight f apostrophe left parenthesis straight x right parenthesis equals 0 rightwards double arrow straight x equals 0 comma space 2
As space minus 3 less or equal than straight x less than 0 space rightwards double arrow space straight x equals negative 3 comma negative 2 comma negative 1 comma 0
At space straight x equals 0 comma space straight f left parenthesis 0 right parenthesis equals 6
straight f left parenthesis straight x right parenthesis space is space maximum space at space straight x equals 0
straight g left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell straight x squared minus 3 straight x plus 6 space semicolon space minus 3 less or equal than straight x less than 0 end cell row cell 1 minus straight x space space space space space space space semicolon space straight x greater or equal than 0 end cell end table close
At space straight x equals 0 comma space LHL equals 0
At space straight x equals 0 comma space RHL equals 1
LHL not equal to RHL
Hence comma space straight g left parenthesis straight x right parenthesis space is space not space continuous space

Answered by Renu Varma | 24th Aug, 2020, 11:01: AM

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