If the parametric curve $x = f ( t ) , \quad y = g ( t )$ satisfies $g ^ { \prime } ( 4 ) = 0$, then it has a horizontal tangent when $t = 4$.

Name: If the parametric curve $x = f ( t ) , \quad y = g ( t )$ satisfies $g ^ { \prime } ( 4 ) = 0$, then it has a horizontal tangent when $t = 4$.
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Question

Quizplus · Accepted Answer

If $g ^ { \prime } ( 4 ) = 0$, then the slope of the tangent line at the point $(f(4),g(4))$ is zero, which means it is a horizontal tangent. Therefore, the statement is true.

If the Parametric Curve x=f(t),y=g(t)x = f ( t ) , \quad y = g ( t )x=f(t),y=g(t)

If the Parametric Curve $x = f ( t ) , \quad y = g ( t )$