Find dx/dt?

Question

y = 4(x^2 – 4x)

(a) Find dy/dt, given x = 5, dx/dt = 8.
I know this one is 192, but I can't figure out part b.

(b) Find dx/dt, given x = 9, dy/dt = 9.
?

Answer 1

The function is y = 4(x^2 - 4x).

• a). To find dy/dt ,

Differentiate The function is y = 4(x^2 - 4x) with respect to ' t '.

dy/dt = 4[ 2x(dx/dt) - 4(dx/dt) ].

Substitute the values x = 5 and dx/dt = 8.

dy/dt = 4[ (2 * 5 * 8) - (4 * 8) ]

= 4[ 80 - 32 ]

= 4 * 48

= 192.

Therfore, dy/dt = 192.

• b). To find dx/dt, substitute the values x = 9 and dy/dt = 9 in dy/dt = 4[ 2x(dx/dt) - 4(dx/dt) ].

9 = 4[ (2 * 9 * dx/dt) - (4 * dx/dt) ]

9/4 = (18 * dx/dt) - (4 * dx/dt)

9/4 =  dx/dt(18 - 4)

9/4 =  14 * dx/dt

dx/dt = [ 9/4 ]/14

dx/dt = 9/( 4 * 14 )

Therefore, dx/dt = 9/56.