Question

A point on the curve, $y=\frac{2}{3}{x}^3+\frac{1}{2}{x}^2$, the tangent at which makes equal angles with axes is

• A. $(\frac{1}{2},\frac{5}{24})$ and $(-1,-\frac{1}{6})$
• B. $(\frac{1}{2},\frac{4}{9})$ and $(-1,0)$
• C. $(\frac{1}{3},\frac{1}{7})$ and $(-3,\frac{1}{2})$
• D. $(\frac{1}{3},\frac{4}{47})$ and $(-1,-\frac{1}{3})$

Answer 1

The correct option is A $(\frac{1}{2},\frac{5}{24})$ and $(-1,-\frac{1}{6})$

The slope of tangent is given by m= dy/dx and m= tan(t) and for the line to make equal angle with axes , m should be 1 or -1.