dy/dx is positive if y increase as x increase and negative if y decreses as x  its mean its a ncrt book question ncrt 1 book chapter 6 page 196
what this statement means and where it would be drive from

Asked by saggugurupal | 17th Aug, 2016, 12:12: PM

Expert Answer:

y space equals f left parenthesis x right parenthesis
fraction numerator d y over denominator d x end fraction space means space rate space of space change space of space straight y space with space respect space to space straight x.

dy over dx space can space either space be space positive space or space negative comma space it space depends space on space whether space function space left curly bracket straight f left parenthesis straight x right parenthesis right curly bracket space is space increasing space or space decreasing.

So space if space straight f left parenthesis straight x right parenthesis space is space increasing space then space dy over dx space is space positive space and space space if space straight f left parenthesis straight x right parenthesis space is space decreasing space then space dy over dx space is space negative.

In space other space words comma
if space straight x subscript 1 space less than space straight x subscript 2 space space space and space space straight f left parenthesis straight x subscript 1 right parenthesis space less than space straight f left parenthesis straight x subscript 2 right parenthesis space then space dy over dx space space is space positive.
if space straight x subscript 1 space less than space straight x subscript 2 space space space and space space straight f left parenthesis straight x subscript 1 right parenthesis space greater than space straight f left parenthesis straight x subscript 2 right parenthesis space then space dy over dx space space is space negative.

The space concept space of space derivative space is space derived space from space the space concepts space of space increasing space function comma space decreasing space functions comma space continuity space and space limit space of space straight a space function.

Answered by Vijaykumar Wani | 18th Aug, 2016, 03:23: PM

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