True or False?
If the parametric curve x = f ( $f$ ), y = g ( $t$ ) satisfies g '( $4$ ) = 0, then it has a horizontal tangent when $t$ = $4$ .

Question

Quizplus · Accepted Answer

If $g' (4) = 0$, then the parametric curve has a horizontal tangent at $t=4$ because the slope of the tangent line is the derivative of the y-coordinate with respect to x, which is equal to $\frac{g'(t)}{f'(t)}$ at any point (t, g(t)). When $t=4$, this fraction becomes $\frac{g'(4)}{f'(4)}$ which is zero divided by some non-zero value, resulting in a slope of zero and hence a horizontal tangent.

True or False? If the Parametric Curve X = F fff

True or False?
If the Parametric Curve X = F $f$