Category: Application of derivative

Calculus

Find the length of the normal at ‘ t ‘ on the curve x = a(t + sint) , y = a(1 – cost).

Q: Find the length of the normal at ‘ t ‘ on the curve x = a(t + sint) ,…

Show that the normal to the curve 5x^5 – 10x^3 + x + 2y + 6 = 0 at P(0, -3) meets the curve again at two points…..

Q: Show that the normal to the curve 5 x5 – 10 x3 + x + 2 y + 6…

Find the equations of the tangent drawn to the curve y^2 – 2 x^3 – 4 y + 8 = 0 from the point (1 , 2).

Q: Find the equations of the tangent drawn to the curve y2 – 2 x3 – 4 y + 8…

A point P is given on the circumference of circle of radius r . The chord QR is parallel to the tangent line at P….

Q: A point P is given on the circumference of circle of radius r . The chord QR is parallel…

Find the equation of normal to the curve y = (1 + x)^y + sin^-1(sin^2x) at x = 0.

Q: Find the equation of normal to the curve y = (1 + x)y + sin-1(sin2x) at x = 0.…

Find all the possible values of the parameter ‘a ‘ so that the function …

Q: Find all the possible values of the parameter ‘a ‘ so that the function, f (x) = x3 –…

$Let \; f(x) = \left\{\begin{array}{ll} -x^3 + \frac{b^3 – b^2 + b – 1}{b^2 + 3b +2} \; , 0 \leq x < 1 \\ 2x - 3 \; , 1 \leq x \leq 3 \end{array} \right.$

Q: \$ \large Let \; f(x) = \left\{\begin{array}{ll} -x^3 + \frac{b^3 – b^2 + b – 1}{b^2 + 3b +2}…

Let a + b = 4, where a < 2, and let g(x) be a differentiable function. If dg/dx > 0 for all x ….

Q: Let a + b = 4, where a < 2, and let g(x) be a differentiable function. If dg/dx…

A conical vessel is to be prepared out of a circular sheet of gold of unit radius. How much sectorial area is to be removed ….

Q: A conical vessel is to be prepared out of a circular sheet of gold of unit radius. How much…

Find a polynomial f(x) of degree 5 which increases in the interval (-∞, 2] and [6, ∞) and decreases in the interval …

Q: Find a polynomial f(x) of degree 5 which increases in the interval (-∞, 2] and [6, ∞) and decreases…

Find the shortest distance between the curves 9x^2 + 9y^2 – 30y + 16 = 0 and y^2 = x^3 ….

Q: Find the shortest distance between the curves 9x2 + 9y2 – 30y + 16 = 0 and y2 =…

Let A(p^2 , – p), B(q^2, q), C(r^2, – r) be the vertices of a triangle ABC. A parallelogram AFDE is drawn with D, E and F on the line segments …..

Q: Let A(p2 , – p), B(q2, q), C(r2, – r) be the vertices of a triangle ABC. A parallelogram…