Suppose y = 2x + 1, where x and y are functions of t.(a) If dx/dt = 6, find dy/dt when x = 4.dydt = (b) If dy/dt = 4, find dx/dt when x = 24.dxdt =

(a) To find dy/dt when x = 4 and dx/dt = 6, we first need to differentiate the given equation y = 2x + 1 with respect to t.

The derivative of y with respect to t (dy/dt) is equal to the derivative of 2x + 1 with respect to t.

Using the chain rule, we get dy/dt = 2(dx/dt).

Substituting dx/dt = 6 into the equation, we get dy/dt = 2*6 = 12.

(b) To find dx/dt when x = 24 and dy/dt = 4, we again start with the derivative dy/dt = 2(dx/dt).

We can rearrange this equation to solve for dx/dt: dx/dt = dy/dt / 2.

Substituting dy/dt = 4 into the equation, we get dx/dt = 4 / 2 = 2.

So, dy/dt = 12 when x = 4 and dx/dt = 6, and dx/dt = 2 when x = 24 and dy/dt = 4.