The curve represented by x=t^5+5 t^3+20 t+7 and y=4 t^3-3 t^2-18 t+3 is decreasing in the interval

Step-by-step solution

x=t^5+5 t^3+20 t+7 aligned & d x d t =5 t^4+15 t^2+20 & and y=4 t^3-3 t^2-18 t+3 d y d t =12 t^2-6 t-18 aligned Now, d y d x = d y d t d x d t = 6 (2 t^3-t-3 ) 5 (t^4+3 t^2+4 ) The curve is decreasing if, d y d x t (-1, 3 2 )