Let and . (a) Determine every real value of for which the curve has a vertical…

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

Let

x(t)=\dfrac{t}{t^{2}+1}

and

y(t)=\arctan t

. (a) Determine every real value of

t

for which the curve has a vertical tangent line. (b) For each such

t

, confirm that

\dfrac{dy}{dt}\neq 0