Question

Find the points on the curve y = x³ at which the slope of the tangent is equal to y-coordinate of the point.

For the curve y = 4x³ – 2x⁵, find all those points at which the tangent passes through the origin.

Find the equation(s) of the tangent(s) to the curve y = (x³ – 1) (x – 2) points where the curve intersects the x-axis.

The total expenditure (in ₹) required for providing the cheap edition of a book for poor and deserving students is given by R(x) = 3x² + 36x, where x is the number of set of books. If the marginal expenditure is defined as ${\frac{d R}{d x}},$ write the marginal expenditure required for 1200 such sets.

Find the equations of the normal to the curve x² = 4y which passes through the point (1, 2).

Can $y=a x+{\frac{b}{a}}$ be a solution of the following differential equation ? $y=x{\frac{d y}{d x}}+{\frac{b}{\frac{d y}{d x}}}$ If no, find the solution of the D.E.

Find the equation of tangent to curves x = sin 3t, y = cos 2t at $:t={\frac{\pi}{4}}\,.$