MEDIUM
JEE Main/Advance
IMPORTANT
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On the interval the function then which one of the following hold good?
(a)is continuous for all values of
(b)is continuous for
(c)assumes all intermediate values from
(d)has a maximum value equal to

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Important Questions on Application of Derivatives
MEDIUM
JEE Main/Advance
IMPORTANT
The coordinates of points(s) at each of which the tangents to the curve cut off on the positive semi axis a line segment half that on the negative semi axis is/are given by:

HARD
JEE Main/Advance
IMPORTANT
The abscissa of the point on the curve , the tangent at which cuts off equal intercepts from the coordinate axes is :

MEDIUM
JEE Main/Advance
IMPORTANT
Equation of a tangent to the curve at the point where the abscissa is is

HARD
JEE Main/Advance
IMPORTANT
Consider the curve represented parametrically by the equation
where where
If denotes the number of points on the curve where the tangent is horizontal and the number of points where the tangent is vertical then-

MEDIUM
JEE Main/Advance
IMPORTANT
If be the equation of a parabola which is touched by the line at the point where . Then

HARD
JEE Main/Advance
IMPORTANT
At the point on the graph of in the first quadrant a normal is drawn. The normal intersects the -axis at the point . If then equal

MEDIUM
JEE Main/Advance
IMPORTANT
A horse runs along a circle with a speed of . A lantern is at the centre of the circle. A fence is there along the tangent to the circle at the point at which the horse starts. The speed with which the shadow of the horse moves along the fence at the moment when it covers of the circle in is

HARD
JEE Main/Advance
IMPORTANT
Equation of the line through the point and tangent to the parabola and secant to the curve is
