a function will have maximum value at x=c if second derivative of f(c) changes sign from a.positive to negative b, negative to positive

Question

a function will have maximum value at x=c if second derivative of f(c) changes sign from    a.positive to negative     b, negative to positive

ghazi · Answer

a function will have maximum when slope changes from positive to negative

ghazi · Answer

|dw:1346254964186:dw|

ghazi · Answer

|dw:1346255004255:dw|

anonymous · Answer

if the second derivative is positive the function is concave up, if the second derivative is negative the function is concave down. Id the second derivative changes sign there a point of inflection

anonymous · Answer

why

ghazi · Answer

you can see the graph above.....from positive slope to negative you'll have maximum value

anonymous · Answer

if f'' is positive then f' is increasing and the other way round

ghazi · Answer

and from negative to positive it's minimum |dw:1346255267547:dw|

anonymous · Answer

I think in your question you have got f'and f'' mixed up

ghazi · Answer

slope is derivative

anonymous · Answer

thnx alot