Find the equation of tangents to the curve y= x³+2x-4, which are perpendicular to line x+14y+3 =0.

Show that semi-vertical angle of a cone of maximum volume and given slant height is cos^-1.

Find the absolute maximum and absolute minimum values of the function f given by

405.

Find the value(s) of x for which y =  is an increasing function.

Find the equations of the tangent and normal to the curve 

If the sum of the lengths of the hypotenuse and a side of a right triangle is given, show that the area of the triangle is maximum when the angle between them is 

Show that the height of the cylinder of maximum volume, which can be inscribed in a sphere of radius R is  Also find the maximum volume. 

Find the equation of the normal at a point on the curve x² = 4y which passes through the point (1, 2). Also, find the equation of the corresponding tangent.

The volume of a sphere is increasing at the rate of 3 cubic centimetres per second. Find the rate of increase of its surface area, when the radius is 2 cm.