Question

If y=3x- x³ and x increases at the rate of 3 units per second, how fast is the slope of the curve changing when x=2 ?

Answer 1

If y=3x- x³ and x increases at the rate of 3 units per second, how fast is the slope of the curve changing when x=2 ?

answer : -36

explanation : it is given that , y = 3x - x³

differentiating respect to x.

i.e., dy/dx = 3 - 3x²

so, the slope of curve y = 3x - x³ is m = 3 - 3x²

a/c to question,

we have to find (dm/dt) at x = 2.

now, m = 3 - 3x²

differentiating m with respect to time,

dm/dt = d(3 - 3x²)/dt = -6x (dx/dt).

given, dx/dt = 3 unit/s and x = 2 unit

so, dm/dt = - 6(2)(3) = -36

hence, rate of change in slope of curve is -36.