Home
Class 12
MATHS
For the curve y=5x-2x^3 , if x increases...

For the curve `y=5x-2x^3` , if `x` increases at the rate of 2 units/sec, then how fast is the slope of the curve changing when `x=3?`

Text Solution

Verified by Experts

`dx/dt = 2`
`y= 5x-2x^3`
`dy/dx= 5 - 6x^2= g(x) `
`(d(g(x)))/(dt) = -12x * 2 = -24x `
at t=3, `= -24 xx 3= -72 `
Answer
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    RD SHARMA|Exercise Solved Examples And Exercises|567 Videos

  • DETERMINANTS

    RD SHARMA|Exercise Solved Examples And Exercises|403 Videos

Similar Questions

Explore conceptually related problems

For the curve y=5x-2x^(3) , if x increases at the rate of 2units/sec, then at x=3 the slope of the curve is changing at ___

If y=7x-x^(3) and x increases at the rate of 4 units per second,how fast is the slope of the curve changing when x=2?

Knowledge Check

  • A point P moves along the curve y=x^(3) . If its abscissa is increasing at the rate of 2 units/ sec, then the rate at which the slop of the tangent at P is increasing when P is at (1,1) , is

    A
    3 units/ sec
    B
    12 units/sec
    C
    24 units/sec
    D
    8 units/sec

  • What is the maximum slope of the curve y=-x^3+3x^2+2x-27 ?

    A
    1
    B
    2
    C
    5
    D
    -23

    • Similar Questions

    Explore conceptually related problems

    If y=x^(3) and x increases at the rate of 3 units per sec; then the rate at which the slope increases when x=3 is.

    A point P moves along the curve y=x^(3) . If its abscissa is increasing at the rate of 2 units/ sec, then the rate at which the slop of the tangent at P is increasing when P is at (1,1) , is

    For curve y=(x^(2))/(2)-2x+5, the rate of change of y is twice the rate of change of x ,then value of x is

    For curve y=(x^(2))/(2)-2x+5 the rate of change of y is twice the rate of change of x ,then value of x is

    For curve y=(x^(2))/(2)-2x+5, the rate of change of y is twice the rate of change of x , then value of x is

    The curve y=sec x tan x+2tan x-sec x and the line y=2 intersect in

    Home
    Profile