At what points of the curve \[y=\frac{2}{3}{{x}^{3}}+\frac{1}{2}{{x}^{2}},\]tangent makes the equal angle with axis [UPSEAT 1999]

\[\left( \frac{1}{2},\,\frac{4}{9} \right)\] and \[\left( -1,\,0 \right)\]

\[\left( \frac{1}{2},\,\frac{5}{24} \right)\] and \[\left( -1,\,-\frac{1}{6} \right)\]

\[\left( \frac{1}{3},\,\frac{1}{7} \right)\] and \[\left( -3,\,\frac{1}{2} \right)\]

\[\left( \frac{1}{3},\,\frac{4}{47} \right)\] and \[\left( -1,\,-\frac{1}{3} \right)\]

At what points of the curve \[y=\frac{2}{3}{{x}^{3}}+\frac{1}{2}{{x}^{

1.	At what points of the curve \[y=\frac{2}{3}{{x}^{3}}+\frac{1}{2}{{x}^{2}},\]tangent makes the equal angle with axis [UPSEAT 1999]
A.	\[\left( \frac{1}{2},\,\frac{5}{24} \right)\] and \[\left( -1,\,-\frac{1}{6} \right)\]
B.	\[\left( \frac{1}{2},\,\frac{4}{9} \right)\] and \[\left( -1,\,0 \right)\]
C.	\[\left( \frac{1}{3},\,\frac{1}{7} \right)\] and \[\left( -3,\,\frac{1}{2} \right)\]
D.	\[\left( \frac{1}{3},\,\frac{4}{47} \right)\] and \[\left( -1,\,-\frac{1}{3} \right)\]
Answer» B. \[\left( \frac{1}{2},\,\frac{4}{9} \right)\] and \[\left( -1,\,0 \right)\]

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