Application of Derivatives
Find the equation of the normals to the curve y=x3+2x+6which are parallel to the line x+14y+4=0.
Determine p such that the length of the such-tangent and sub-normal is equal for the curve y=epx+px at the point (0,1)˙
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 is ay2=bx−1, then the value of (a+b) is____
A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the maximum length of the hypotenuse is (a32+b32)23 .
A running track of 440 ft is to be laid out enclosing a football field, the shape of which is a rectangle with a semi-circle at each end. If the area of the rectangular portion is to be maximum, then find the length of its sides.