हिंदी

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

प्रश्न

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

उत्तर

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

On differentiating with respect to x, we get:

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Application of Derivatives - Exercise 6.3 [पृष्ठ २१२]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 6 Application of Derivatives
Exercise 6.3 | Q 14.2 | पृष्ठ २१२

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

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


The equation of tangent at (2, 3) on the curve y2 = ax3 + b is y = 4x – 5. Find the values of a and b.


Find the equation of tangents to the curve y= x3 + 2x – 4, which are perpendicular to line x + 14y + 3 = 0.


Show that the equation of normal at any point t on the curve x = 3 cos t – cos3t and y = 3 sin t – sin3t is 4 (y cos3t – sin3t) = 3 sin 4t


Find the equation of all lines having slope −1 that are tangents to the curve  `y = 1/(x -1), x != 1`


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


Find the point on the curve y = x2 where the slope of the tangent is equal to the x-coordinate of the point ?


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 x4 − bx3 + 13x2 − 10x + 5 at (0, 5)  ?


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


Find the equation of the tangent line to the curve y = x2 − 2x + 7 which is parallel to the line 2x − y + 9 = 0 ?


Find the angle of intersection of the following curve  x2 = 27y and y2 = 8x ?


Find the angle of intersection of the following curve x2 + y2 = 2x and y2 = x ?


Show that the following curve intersect orthogonally at the indicated point x2 = y and x3 + 6y = 7 at (1, 1) ?


Prove that the curves xy = 4 and x2 + y2 = 8 touch each other ?


Find the slope of the normal at the point 't' on the curve \[x = \frac{1}{t}, y = t\] ?


Write the coordinates of the point on the curve y2 = x where the tangent line makes an angle \[\frac{\pi}{4}\] with x-axis  ?


Write the angle made by the tangent to the curve x = et cos t, y = et sin t at \[t = \frac{\pi}{4}\] with the x-axis ?


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


The equation of the normal to the curve y = x(2 − x) at the point (2, 0) is ________________ .


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


The point at the curve y = 12x − x2 where the slope of the tangent is zero will be _____________ .


The point on the curve y = 6x − x2 at which the tangent to the curve is inclined at π/4 to the line x + y= 0 is __________ .


Find the condition for the curves `x^2/"a"^2 - y^2/"b"^2` = 1; xy = c2 to interest orthogonally.


Find the equation of all the tangents to the curve y = cos(x + y), –2π ≤ x ≤ 2π, that are parallel to the line x + 2y = 0.


The point on the curve y2 = x, where the tangent makes an angle of `pi/4` with x-axis is ______.


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 points at which the tangents to the curve y = x3 – 12x + 18 are parallel to x-axis are ______.


The point on the curves y = (x – 3)2 where the tangent is parallel to the chord joining (3, 0) and (4, 1) is ____________.


The distance between the point (1, 1) and the tangent to the curve y = e2x + x2 drawn at the point x = 0


Find a point on the curve y = (x – 2)2. at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).


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


Tangent is drawn to the ellipse `x^2/27 + y^2 = 1` at the point `(3sqrt(3) cos theta, sin theta), 0 < 0 < 1`. The sum of the intercepts on the axes made by the tangent is minimum if 0 is equal to


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


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


An edge of variable cube is increasing at the rate of 3 cm/s. The volume of the cube increasing fast when the edge is 10 cm long is ______ cm3/s.


The number of values of c such that the straight line 3x + 4y = c touches the curve `x^4/2` = x + y is ______.


For the curve y2 = 2x3 – 7, the slope of the normal at (2, 3) is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×