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

The correct Answer is:
`-72` units/se.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    OSWAAL PUBLICATION|Exercise TOPIC - I RATE OF CHANGE OF QUANTITIES (LONG ANSWER TYPE QUESTIONS -II)|8 Videos

  • APPLICATIONS OF DERIVATIVES

    OSWAAL PUBLICATION|Exercise TOPIC -2 TANGENTS AND NORMALS (SHORT ANSWER TYPE QUESTIONS-I)|2 Videos

  • APPLICATION OF INTEGRALS

    OSWAAL PUBLICATION|Exercise Long Answer Type Questions - II|25 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OSWAAL PUBLICATION|Exercise MVT AND ROLLE.S THEOREM ( SHORT ANSWER TYPE QUESTIONS-II)|5 Videos

Similar Questions

Explore conceptually related problems

If equation of the curve is y^2=4x then find the slope of normal to the curve

Find the asymptotes of the curve xy-3y-2x=0.

Knowledge Check

  • A point is moving on y=4-2x^(2) . The x coordiante of the point is decreasing at the rate of 5 units per second. Then the rate at which y coordinate of the point is changing when the point is at (1,2) is

    A
    5 units/sec
    B
    10 units/sec
    C
    15 units/sec
    D
    20 units/sec

  • The slope of the tangent to a curve, y = f(x) at (x, f(x)) is 2x+1. If the curve passes through the point (1,2) , then the area of the region bounded by the curve, the x -axis and the line x=1

    A
    `5/6`
    B
    `2/3`
    C
    `1/3`
    D
    `1/6`

  • If m is the slope of the tangent to the curve, e^(y) =1 +x^(2) , then,

    A
    `|m| gt 1`
    B
    `m lt 1`
    C
    `|m| lt 1`
    D
    `|m| le 1`

    • Similar Questions

    Explore conceptually related problems

    For the curve y = 4x^(3) - 2x^(5) , find all the points at which the tangent passes through the origin.

    For the curve y = 4x^(3) – 2x^(5) , find all the points at which the tangent passes through the origin.

    Find the slope of the tangent to the curve y= x^(3)-x at x=2

    The normal at the point (1,1) on the curve 2y + x^(2) = 3 is

    Area bounded by the curve y=x^3 , the x-axis and the ordinates x=-2 and x=1 , is :

    Home
    Profile