English

Find the Slope of the Tangent to the Curve Y = 3x4 − 4x at X = 4. - Mathematics

Advertisements
Advertisements

Question

Find the slope of the tangent to the curve y = 3x4 − 4x at x = 4.

Advertisements

Solution

The given curve is y = 3x4 − 4x.

Then, the slope of the tangent to the given curve at x = 4 is given by,

shaalaa.com
  Is there an error in this question or solution?
Chapter 6: Application of Derivatives - Exercise 6.3 [Page 211]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 6 Application of Derivatives
Exercise 6.3 | Q 1 | Page 211

RELATED QUESTIONS

Find the equations of the tangent and normal to the curve x = a sin3θ and y = a cos3θ at θ=π/4.


Find the equation of the normal at a point on the curve x2 = 4y which passes through the point (1, 2). Also find the equation of the corresponding tangent.


Find the slope of the normal to the curve x = acos3θy = asin3θ at `theta = pi/4`


Find the equation of the normal to curve y2 = 4x at the point (1, 2).


Show that the normal at any point θ to the curve x = a cosθ + a θ sinθ, y = a sinθ – aθ cosθ is at a constant distance from the origin.


Find the slope of the tangent and the normal to the following curve at the indicted point  x = a (θ − sin θ), y = a(1 − cos θ) at θ = π/2 ?


Find the points on the curve y2 = 2x3 at which the slope of the tangent is 3 ?


At what points on the circle x2 + y2 − 2x − 4y + 1 = 0, the tangent is parallel to x-axis?


Find the points on the curve x2 + y2 = 13, the tangent at each one of which is parallel to the line 2x + 3y = 7 ?


Find the points on the curve \[\frac{x^2}{9} + \frac{y^2}{16} = 1\] at which the tangent is  parallel to y-axis ?


Find the equation of the normal to y = 2x3 − x2 + 3 at (1, 4) ?


Find the equation of the tangent and the normal to the following curve at the indicated point xy = c2 at \[\left( ct, \frac{c}{t} \right)\] ?


Find the equation of the tangent line to the curve y = x2 + 4x − 16 which is parallel to the line 3x − y + 1 = 0 ?


Find the equation of the tangent line to the curve y = x2 − 2x + 7 which perpendicular to the line 5y − 15x = 13. ?


Prove that \[\left( \frac{x}{a} \right)^n + \left( \frac{y}{b} \right)^n = 2\] touches the straight line \[\frac{x}{a} + \frac{y}{b} = 2\] for all n ∈ N, at the point (a, b) ?


At what points will be tangents to the curve y = 2x3 − 15x2 + 36x − 21 be parallel to x-axis ? Also, find the equations of the tangents to the curve at these points ?


Find the equation of  the tangents to the curve 3x2 – y2 = 8, which passes through the point (4/3, 0) ?


Find the angle of intersection of the following curve  y = x2 and x2 + y2 = 20  ?


Show that the curves 4x = y2 and 4xy = k cut at right angles, if k2 = 512 ?


Show that the curves 2x = y2 and 2xy = k cut at right angles, if k2 = 8 ?


Show that the curves \[\frac{x^2}{a^2 + \lambda_1} + \frac{y^2}{b^2 + \lambda_1} = 1 \text { and } \frac{x^2}{a^2 + \lambda_2} + \frac{y^2}{b^2 + \lambda_2} = 1\] intersect at right angles ?


If the tangent line at a point (x, y) on the curve y = f(x) is parallel to y-axis, find the value of \[\frac{dx}{dy}\] ?


Write the equation on the tangent to the curve y = x2 − x + 2 at the point where it crosses the y-axis ?


Any tangent to the curve y = 2x7 + 3x + 5 __________________ .


The slope of the tangent to the curve x = t2 + 3t − 8, y = 2t2 − 2t − 5 at the point (2, −1) is _____________ .


The normal at the point (1, 1) on the curve 2y + x2 = 3 is _____________ .


Find the equation of tangent to the curve `y = sqrt(3x -2)` which is parallel to the line 4x − 2y + 5 = 0. Also, write the equation of normal to the curve at the point of contact.


Find the co-ordinates of the point on the curve `sqrt(x) + sqrt(y)` = 4 at which tangent is equally inclined to the axes


Prove that the curves y2 = 4x and x2 + y2 – 6x + 1 = 0 touch each other at the point (1, 2)


Show that the line `x/"a" + y/"b"` = 1, touches the curve y = b · e– x/a at the point where the curve intersects the axis of y


The curve y = `x^(1/5)` has at (0, 0) ______.


The equation of tangent to the curve y(1 + x2) = 2 – x, where it crosses x-axis is ______.


For which value of m is the line y = mx + 1 a tangent to the curve y2 = 4x?


The two curves x3 - 3xy2 + 5 = 0 and 3x2y - y3 - 7 = 0


The tangent to the curve y = 2x2 - x + 1 is parallel to the line y = 3x + 9 at the point ____________.


Tangents to the curve x2 + y2 = 2 at the points (1, 1) and (-1, 1) are ____________.


The points at which the tangent passes through the origin for the curve y = 4x3 – 2x5 are


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×