5. For what values of t is this concave up

Calculus
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x = 5 sin t,    y = 6 cos t,    0 < t < 2π

for what values is this concave up

Apr 4th, 2015

Parametric equations: x = 5 sin t; y = 6cos t; 0 < t < 2 π.

Find the first derivative of y by x: y'x = y't / x't = ( – 6sin t )/( 5 cos t) = (– 6/5) tan t.

Find the second derivative of y by x: y''xx = (y'x )'t / x't = ( –6/5 cos–2 t) / 5 cos t= –6/25 cos–3 t

y''xx = –6/25 cos–3 t > 0 if cos t < 0 . The curve is concave upward if t is in the interval (π/2 , 3π/2).


Apr 4th, 2015

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