E-RC04 · Two linked outputs and a compatibility check
Quantities x, y and z depend on time t, with \(y=(x^2+1)^2\) and \(z=(3x+1)^3\). At an instant when \(\displaystyle x=2\), \(\displaystyle \frac{dy}{dt}= 80\).
Find \(\displaystyle \frac{dx}{dt}\) at this instant.
Find \(\displaystyle \frac{dz}{dt}\) at the same instant.
At another instant \(\displaystyle x=0\) and \(\displaystyle \frac{dx}{dt}\) is finite. Can \(\displaystyle \frac{dy}{dt}\) equal 5 at that instant? Explain fully.
Complete-answer checking, worked solutions and indicative written criteria.
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