Mathematics

Mathematics

Problem

For a parametric curve given by x=f(t)x=f(t) and y=g(t)y=g(t), which of the following conditions at t=t0t=t_0 guarantees that the tangent to the curve is vertical? a) f′(t0)=0 and g′(t0)=0f'(t_0)=0 \text{ and } g'(t_0)=0 b) ∣g′(t0)f′(t0)∣→∞\displaystyle \left|\frac{g'(t_0)}{f'(t_0)}\right| \to \infty c) f′(t0)=0 and g′(t0)≠0f'(t_0)=0 \text{ and } g'(t_0)\ne 0 d) f′(t0)≠0 and g′(t0)=0f'(t_0)\ne0 \text{ and } g'(t_0)=0

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