MEDIUM
JEE Main/Advance
IMPORTANT
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On the interval I=-2,2, the function fx=x+1e-1x+1xx00x=0 then which one of the following hold good?

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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 y=x3-3x2-7x+6 cut off on the positive semi axis OX a line segment half that on the negative semi axis OY is/are given by:
HARD
JEE Main/Advance
IMPORTANT
The abscissa of the point on the curve xy=a+x, the tangent at which cuts off equal intercepts from the coordinate axes is a>0:
MEDIUM
JEE Main/Advance
IMPORTANT
Equation of a tangent to the curve ycotx=y3tanx at the point where the abscissa is π4 is
HARD
JEE Main/Advance
IMPORTANT
Consider the curve represented parametrically by the equation
x=t3-4t2-3t where y=2t2+3t-5 where tR

If H denotes the number of points on the curve where the tangent is horizontal and V the number of points where the tangent is vertical then-
MEDIUM
JEE Main/Advance
IMPORTANT
If y=f(x) be the equation of a parabola which is touched by the line y=xat the point where x=1. Then
HARD
JEE Main/Advance
IMPORTANT
At the point Pa,an on the graph of y=xnnN in the first quadrant a normal is drawn. The normal intersects the Y-axis at the point 0, b. If lima0b=12, then n equal
MEDIUM
JEE Main/Advance
IMPORTANT
A horse runs along a circle with a speed of 20 km/h. 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 18 of the circle in km/h is
HARD
JEE Main/Advance
IMPORTANT
Equation of the line through the point 12,2 and tangent to the parabola y=-x22+2 and secant to the curve y=4-x2 is