60 points. The critical points of the given equation is (1 and 3) or (-1 and 3) ?
||x - 1| - 2| = |x - 3|
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Answered by
2
critical points are those points in case if modulus function where the derivative is not defined...
so critical points are {1 ,3}
_____________________________
hope it will help u
so critical points are {1 ,3}
_____________________________
hope it will help u
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Divyankasc:
didn't understand
what is derivative not defined
derivative of modulus function is not defined at the point which i have shown
derivative means differentiation
u know geometrical meaning of derivative it means tangent to curve ....and if u remember the graph of absolute value u will get my answer...
u can see graph of modulus function is like ". V "
at sharp point derivative is not defined this is critical point
I seeee
Answered by
3
critical points means ,any points in the curve where , graph change own property.
in other way , we can say that
any points where , f'(x) = 0 or undefined is known as critical points .
see above graph , here you can see that
curve at x = 3 and x = 1
change own property ,
at x = 1
left side of x = 1 is an increasing graph ( upward or positive slope )
right side of x = 1 is a decreasing graph ( downward or negative slope )
similarly ,
at x = 3
left side decreasing and right side increasing .
so, here x = 1 and x = 3 is critical points .
in other way , we can say that
any points where , f'(x) = 0 or undefined is known as critical points .
see above graph , here you can see that
curve at x = 3 and x = 1
change own property ,
at x = 1
left side of x = 1 is an increasing graph ( upward or positive slope )
right side of x = 1 is a decreasing graph ( downward or negative slope )
similarly ,
at x = 3
left side decreasing and right side increasing .
so, here x = 1 and x = 3 is critical points .
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i hope its help you
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