English

Find the Equations of the Tangent and Normal to the Given Curves at the Indicated Points: Y = X4 − 6x3 + 13x2 − 10x + 5 at (1, 3) - Mathematics

Advertisements
Advertisements

Question

Find the equations of the tangent and normal to the given curves at the indicated points:

y = x4 − 6x3 + 13x2 − 10x + 5 at (1, 3)

Advertisements

Solution

The equation of the curve is y = x4 − 6x3 + 13x2 − 10x + 5.

On differentiating with respect to x, we get:

shaalaa.com
  Is there an error in this question or solution?
Chapter 6: Application of Derivatives - Exercise 6.3 [Page 212]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 6 Application of Derivatives
Exercise 6.3 | Q 14.2 | Page 212

RELATED QUESTIONS

Find the slope of the tangent to the curve y = (x -1)/(x - 2), x != 2 at x = 10.


Find the slope of the tangent to the curve y = x3 − 3x + 2 at the point whose x-coordinate is 3.


Find the equations of all lines having slope 0 which are tangent to the curve  y =   `1/(x^2-2x + 3)`


Find the equations of the tangent and normal to the given curves at the indicated points:

y = x3 at (1, 1)


Find the equations of the tangent and normal to the given curves at the indicated points:

x = cos ty = sin t at  t = `pi/4`


Find the points on the curve x2 + y2 − 2x − 3 = 0 at which the tangents are parallel to the x-axis.


Find the equations of the tangent and normal to the parabola y2 = 4ax at the point (at2, 2at).


The slope of the normal to the curve y = 2x2 + 3 sin x at x = 0 is

(A) 3

(B) 1/3

(C) −3

(D) `-1/3`


The line y = x + 1 is a tangent to the curve y2 = 4x at the point

(A) (1, 2)

(B) (2, 1)

(C) (1, −2)

(D) (−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 points on the curve y = `4x^3 - 3x + 5` at which the equation of the tangent is parallel to the x-axis.


Find the slope of the tangent and the normal to the following curve at the indicted point y = 2x2 + 3 sin x at x = 0 ?


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 equation of the tangent and the normal to the following curve at the indicated point x4 − bx3 + 13x2 − 10x + 5 at (0, 5)  ?


Find the equation of the tangent and the normal to the following curve at the indicated point  \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \text { at } \left( a\sec\theta, b\tan\theta \right)\] ?


 Find the equation of the tangent and the normal to the following curve at the indicated point  x2 = 4y at (2, 1) ?


Find the equation of the tangent and the normal to the following curve at the indicated points:

x = 3cosθ − cos3θ, y = 3sinθ − sin3θ? 


Find the equation of the normal to the curve x2 + 2y2 − 4x − 6y + 8 = 0 at the point whose abscissa is 2 ?


Show that the following set of curve intersect orthogonally y = x3 and 6y = 7 − x?


Show that the following curve intersect orthogonally at the indicated point x2 = 4y and 4y + x2 = 8 at (2, 1) ?


Find the point on the curve y = x2 − 2x + 3, where the tangent is parallel to x-axis ?


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


If the tangent to a curve at a point (xy) is equally inclined to the coordinates axes then write the value of \[\frac{dy}{dx}\] ?


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 of the normal to the curve y = x + sin x cos x at \[x = \frac{\pi}{2}\] ?


Write the equation of the normal to the curve y = cos x at (0, 1) ?


The point on the curve y2 = x where tangent makes 45° angle with x-axis is ____________________ .


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


The point on the curve 9y2 = x3, where the normal to the curve makes equal intercepts with the axes is

(a) \[\left( 4, \frac{8}{3} \right)\]

(b) \[\left( - 4, \frac{8}{3} \right)\]

(c) \[\left( 4, - \frac{8}{3} \right)\]

(d) none of these

 


The two curves x3 – 3xy2 + 2 = 0 and 3x2y – y3 = 2 ______.


Find the angle of intersection of the curves y = 4 – x2 and y = x2.


At what points on the curve x2 + y2 – 2x – 4y + 1 = 0, the tangents are parallel to the y-axis?


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


Find points on the curve `x^2/9 + "y"^2/16` = 1 at which the tangent is parallel to y-axis. 


The number of common tangents to the circles x2 + y2 – 4x – 6x – 12 = 0 and x2 + y2 + 6x + 18y + 26 = 0 is


The Slope of the normal to the curve `y = 2x^2 + 3 sin x` at `x` = 0 is


The slope of the tangentto the curve `x= t^2 + 3t - 8, y = 2t^2 - 2t - 5` at the point `(2, -1)` is


Find the equation to the tangent at (0, 0) on the curve y = 4x2 – 2x3


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×