Answer
a) dy/dt = 26
b) dx/dt = 4/7
Work Step by Step
$ y = 3x^2 - 5x $
$\frac{d}{dt} (y) = \frac{d}{dt} ( 3x^2 - 5x) $
$\frac{dy}{dt} = 6x \frac{dx}{dt} - 5\frac{dx}{dt} = (6x -5)\frac{dx}{dt} $
a) find dy/dt when x = 3 and dx/dt = 2
$\frac{dy}{dt} = 6x \frac{dx}{dt} - 5\frac{dx}{dt} = (6x -5)\frac{dx}{dt} $
$\frac{dy}{dt} = 6(3)(2) - 5(2) = 36 - 10 = 26 $
b) find dx/dt when x = 2 and dy/dt = 4
$ 4 = (6(2)-5) \frac{dx}{dt}$
$\frac{dx}{dt} = 4/7 $
