Find the points on the curve $x ( t ) = 3 - t ^ { 2 } , y ( t ) = t ^ { 2 } + 4 t$ where the tangent line is horizontal.

A)(-4,-1)
B)(-1,4)
C)(-1,-4)
D)(1,-4)
E)(1,4)

Question

Find the points on the curve $x ( t ) = 3 - t ^ { 2 } , y ( t ) = t ^ { 2 } + 4 t$ where the tangent line is horizontal.

A)(-4,-1)
B)(-1,4)
C)(-1,-4)
D)(1,-4)
E)(1,4)

Quizplus · Accepted Answer

The tangent line is horizontal where the derivative of y with respect to t is zero. The derivative $dy/dt = 2t + 4$. Setting $2t + 4 = 0$ gives $t = -2$. Substituting $t = -2$ into the parametric equations gives the point $(-1, -4)$.

Find the Points on the Curve x(t)=3−t2,y(t)=t2+4tx ( t ) = 3 - t ^ { 2 } , y ( t ) = t ^ { 2 } + 4 tx(t)=3−t2,y(t)=t2+4t

Find the Points on the Curve $x ( t ) = 3 - t ^ { 2 } , y ( t ) = t ^ { 2 } + 4 t$