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At what points of curve y = (2)/(3) x^(3...

At what points of curve `y = (2)/(3) x^(3) + (1)/(2) x^(2)`, the tangent makes equal angle with the axis ? a)`((1)/(2),(5)/(24))and (-1, -(1)/(6))` b)`((1)/(2),(4)/(9))and (-1,0)` c)`((1)/(3),(1)/(7))and (-3,(1)/(2))` d)`((1)/(3),(4)/(47))and (-1,-(1)/(3))`

A

`((1)/(2),(5)/(24))and (-1, -(1)/(6))`

B

`((1)/(2),(4)/(9))and (-1,0)`

C

`((1)/(3),(1)/(7))and (-3,(1)/(2))`

D

`((1)/(3),(4)/(47))and (-1,-(1)/(3))`

Text Solution

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The correct Answer is:
A
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