A curve parametrically given by `x=t+t^(3)" and "y=t^(2)," where "t in R." For what vlaue(s) of t is "(dy)/(dx)=(1)/(2)`?

Options

A. `1//3`
B. 2
C. 3
D. 1

Explanation

To solve the problem, we need to find the values of \( t \) for which \( \frac{dy}{dx} = \frac{1}{2} \) given the parametric equations \( x = t + t^3 \) and \( y = t^2 \).

### Step-by-Step Solution:

1. **Write down the parametric equations:**
\[ x = t + t^3 \]
...