Advertisements
Advertisements
Question
The curve y = `x^(1/5)` has at (0, 0) ______.
Options
A vertical tangent (parallel to y-axis)
A horizontal tangent (parallel to x-axis)
An oblique tangent
No tangent
Solution
The curve y = `x^(1/5)` has at (0, 0) a vertical tangent (parallel to y-axis).
Explanation:
Equation of curve is y = `x^(1/5)`
Differentiating w.r.t. x,
We get `"dy"/"dx" = 1/5 x^((-4)/5)`
At x = 0 `"dy"/"dx" = 1/5(0)^((-4)/5)`
= `1/5 xx 1/0 = oo`
`"dy"/"dx" = oo`
∴ The tangent is parallel to y-axis.
APPEARS IN
RELATED QUESTIONS
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
For the curve y = 4x3 − 2x5, find all the points at which the tangents passes through the origin.
Find the equation of the normal at the point (am2, am3) for the curve ay2 = x3.
The line y = mx + 1 is a tangent to the curve y2 = 4x if the value of m is
(A) 1
(B) 2
(C) 3
(D) 1/2
Find the equations of the tangent and the normal, to the curve 16x2 + 9y2 = 145 at the point (x1, y1), where x1 = 2 and y1 > 0.
Find the points on the curve y = `4x^3 - 3x + 5` at which the equation of the tangent is parallel to the x-axis.
If the tangent to the curve y = x3 + ax + b at (1, − 6) is parallel to the line x − y + 5 = 0, find a and b ?
Who that the tangents to the curve y = 7x3 + 11 at the points x = 2 and x = −2 are parallel ?
Find the equation of the tangent and the normal to the following curve at the indicated point y = 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 \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \text { at } \left( x_1 , y_1 \right)\] ?
Find the equation of the tangent and the normal to the following curve at the indicated point \[x^\frac{2}{3} + y^\frac{2}{3}\] = 2 at (1, 1) ?
Find the equation of the tangent and the normal to the following curve at the indicated points x = a(θ + sinθ), y = a(1 − cosθ) at θ ?
Find the equation of the tangent and the normal to the following curve at the indicated points x = asect, y = btant at t ?
Find the angle of intersection of the following curve \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\] and x2 + y2 = ab ?
Show that the curves 2x = y2 and 2xy = k cut at right angles, if k2 = 8 ?
Find the condition for the following set of curve to intersect orthogonally \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \text { and } xy = c^2\] ?
Write the equation on the tangent to the curve y = x2 − x + 2 at the point where it crosses the y-axis ?
Write the slope of the normal to the curve \[y = \frac{1}{x}\] at the point \[\left( 3, \frac{1}{3} \right)\] ?
Find the equation of tangent to the curve y = x2 +4x + 1 at (-1 , -2).
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.
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
Find an angle θ, 0 < θ < `pi/2`, which increases twice as fast as its sine.
The slope of tangent to the curve x = t2 + 3t – 8, y = 2t2 – 2t – 5 at the point (2, –1) is ______.
For which value of m is the line y = mx + 1 a tangent to the curve y2 = 4x?
`"sin"^"p" theta "cos"^"q" theta` attains a maximum, when `theta` = ____________.
The slope of the tangent to the curve x = a sin t, y = a{cot t + log(tan `"t"/2`)} at the point ‘t’ is ____________.
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
