ANSWER
[tex] \frac{1}{2} [/tex]
EXPLANATION
The given parametric curve has equation:
[tex]x = {t}^{2} + 2t[/tex]
and
[tex]y = {t}^{2} + 1[/tex]
Let us differentiate each equationtion with respect to t.
[tex] \frac{dx}{dt} = 2t + 2[/tex]
and
[tex] \frac{dy}{dt} = 2t[/tex]
The slope function is given by:
[tex] \frac{dy}{dx} = \frac{ \frac{dy}{dt} }{ \frac{dx}{dt} } [/tex]
This implies that:
[tex] \frac{dy}{dx} = \frac{2t}{2t + 2} [/tex]
At t=1,
[tex] \frac{dy}{dx} = \frac{2(1)}{2(1)+ 2} [/tex]
[tex] \frac{dy}{dx} = \frac{2}{4} [/tex]
[tex] \frac{dy}{dx} = \frac{1}{2} [/tex]
The correct choice is A.
