class 12

Math

Calculus

Application of Derivatives

Find minimum and maximum value of $3cosx+5sin(x−6π )$

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Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle is one-third that of the cone and the greatest volume of cylinder is $274 πh_{3}tan_{2}α˙$

Find the approximate change in the volume V of a cube of side x meters caused by increasing the side by 2%.

Find the equations of the tangent and normal to the hyperbola $a_{2}x_{2} −b_{2}y_{2} =1$. at the point $(x_{0},y_{0})$

For the curve $y=4x_{3}−2x_{5},$find all the points at which the tangent passes through the origin.

Find the approximate change in the volume V of a cube of side x metres caused by increasing the side by 1%.

Find the equation of tangents to the curve $y=cos(x+y),−2π≤x≤2π$that are parallel to the line $x+2y=0$.

Find the equation of all lines having slope 2 which are tangents to the curve $y=x−31 ,x=3$

Find the equation of tangent to the curve given by$x=asin_{3}t,y=bcos_{3}t$ ... (1)at a point where $t=2π $.