Advertisements
Advertisements
प्रश्न
Find points at which the tangent to the curve y = x3 − 3x2 − 9x + 7 is parallel to the x-axis.
उत्तर
When x = 3, y = (3)3 − 3 (3)2 − 9 (3) + 7 = 27 − 27 − 27 + 7 = −20.
When x = −1, y = (−1)3 − 3 (−1)2 − 9 (−1) + 7 = −1 − 3 + 9 + 7 = 12.
Hence, the points at which the tangent is parallel to the x-axis are (3, −20) and
(−1, 12).
APPEARS IN
संबंधित प्रश्न
Find the slope of the tangent and the normal to the following curve at the indicted point \[y = \sqrt{x^3} \text { at } x = 4\] ?
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 x2 + y2 = 13, the tangent at each one of which is parallel to the line 2x + 3y = 7 ?
Find the points on the curve 2a2y = x3 − 3ax2 where the tangent is parallel to x-axis ?
At what points on the curve y = x2 − 4x + 5 is the tangent perpendicular to the line 2y + x = 7?
Find the points on the curve\[\frac{x^2}{4} + \frac{y^2}{25} = 1\] at which the tangent is parallel to the y-axis ?
Find the points on the curve y = x3 where the slope of the tangent is equal to the x-coordinate of the point ?
Find the equation of the tangent to the curve \[\sqrt{x} + \sqrt{y} = a\] at the point \[\left( \frac{a^2}{4}, \frac{a^2}{4} \right)\] ?
Find the equation of the tangent and the normal to the following curve at the indicated point y = x2 + 4x + 1 at x = 3 ?
Find the equation of the tangent and the normal to the following curve at the indicated point\[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \text{ at }\left( a\cos\theta, b\sin\theta \right)\] ?
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 xy = c2 at \[\left( ct, \frac{c}{t} \right)\] ?
Find the equation of the tangent and the normal to the following curve at the indicated point \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \text { at } \left( x_1 , y_1 \right)\] ?
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 a normal to the curve y = x loge x which is parallel to the line 2x − 2y + 3 = 0 ?
Find the equations of all lines having slope 2 and that are tangent to the curve \[y = \frac{1}{x - 3}, x \neq 3\] ?
Find the equation of the tangent to the curve x = sin 3t, y = cos 2t at
\[t = \frac{\pi}{4}\] ?
Find the angle of intersection of the following curve y2 = x and x2 = y ?
Find the angle of intersection of the following curve \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\] and x2 + y2 = ab ?
Find the angle of intersection of the following curve x2 + 4y2 = 8 and x2 − 2y2 = 2 ?
Show that the following set of curve intersect orthogonally x2 + 4y2 = 8 and x2 − 2y2 = 4 ?
Prove that the curves xy = 4 and x2 + y2 = 8 touch each other ?
The point on the curve y2 = x where tangent makes 45° angle with x-axis is ______________ .
The point on the curve y2 = x where tangent makes 45° angle with x-axis is ____________________ .
The equation of the normal to the curve 3x2 − y2 = 8 which is parallel to x + 3y = 8 is ____________ .
The normal to the curve x2 = 4y passing through (1, 2) is _____________ .
Find the angle of intersection of the curves \[y^2 = 4ax \text { and } x^2 = 4by\] .
Find the equation of tangent to the curve y = x2 +4x + 1 at (-1 , -2).
Find the equation of a tangent and the normal to the curve `"y" = (("x" - 7))/(("x"-2)("x"-3)` at the point where it cuts the x-axis
Find the angle of intersection of the curves y2 = 4ax and x2 = 4by.
Show that the equation of normal at any point on the curve x = 3cos θ – cos3θ, y = 3sinθ – sin3θ is 4 (y cos3θ – x sin3θ) = 3 sin 4θ
The abscissa of the point on the curve 3y = 6x – 5x3, the normal at which passes through origin is ______.
Find the co-ordinates of the point on the curve `sqrt(x) + sqrt(y)` = 4 at which tangent is equally inclined to the axes
The tangent to the curve y = e2x at the point (0, 1) meets x-axis at ______.
For which value of m is the line y = mx + 1 a tangent to the curve y2 = 4x?
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).
If `tan^-1x + tan^-1y + tan^-1z = pi/2`, then
The line is y = x + 1 is a tangent to the curve y2 = 4x at the point.
The normal at the point (1, 1) on the curve `2y + x^2` = 3 is
