x = 5 sin t, y = 6 cos t, 0 < t < 2π
for what values is this concave up
equations: x = 5 sin t;
y = 6cos t; 0 < t < 2 π.
the first derivative of y by x: y'x
= ( – 6sin t )/( 5 cos
t) = (–
the second derivative of y by x: y''xx
= ( –6/5 cos–2
/ 5 cos t=
= –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).
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