Application of Derivatives
Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is 32R. Also find the maximum volume.
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be a continuous and differentiable function. Then show that
If the tangent at any point (4m2,8m2)
is a normal to the curve x3−y2=0
, then find the value of m˙
The latest edge of a regular hexagonal pyramid is 1cm˙
If the volume is maximum, then find its height.
The tangent to the parabola y=x2
has been drawn so that the abscissa x0
of the point of tangency belongs to the interval [1,2]. Find x0
for which the triangle bounded by the tangent, the axis of ordinates, and the straight line y=x02
has the greatest area.
Let f(x)=−sin3x+3sin2x+5 on [0,2π] . Find the local maximum and local minimum of f(x)˙
A curve is defined parametrically be equations x=t2andy=t3
. A variable pair of perpendicular lines through the origin O
meet the curve of PandQ
. If the locus of the point of intersection of the tangents at PandQ
then the value of (a+b)
Find the minimum value of (x1−x2)2+(20x12−(17−x2)(x2−13))2 where x1∈R+,x2∈(13,17).
Show that the tangent to the curve 3xy2−2x2y=1at(1,1)
meets the curve again at the point (−516,−201)˙