Richard P. answered • 03/28/21

PhD in Physics with 10+ years tutoring experience in STEM subjects

The correct answer is d) t = 1.525

The route to this result involves a number of steps.

First dy/dx = is easily obtained from the ratio of dy/dt and dx/dt as

dy/dt = (1/3) t^{5} - (2/3) t^{2} define Q as dy/dt

What is needed is dQ/dx (the second derivative of y wrt x)

dQ/dx = (dQ/dt) ( dt/dx) but dt/dx = 1/( 3 t^{2}) so

dQ/dx = (5/9) t^{2} -(4/3) /t

Setting this equal to 1 results in a cubic equation with solution t = 1.525