Question

Determine the value of dy/dt at x = 2 when
y = 3x^2− 5x
and dx/dt = 3.

Answer 1

you need to differentiate.. but it looks like it needs to be dy/dx and not dy/dt

the general rule is if

\[y = x^n.... then... \frac{dy}{dx} = n \times x^{n -1}\]

using that rule you will have

\[\frac{dy}{dx} = 3 \times 2 x^{2 -1} - 5 \times 1 \times x^{1-1}\]

this simplifies to

\[\frac{dy}{dx} = 6x - 5\]

so for the 1st part substitute x = 2 into the above equation and solve for dy/dx


The next part is let dy/dx = 3 and solve for x

so you will have

3 = 6x - 5

solve for x

hope it helps