class 12

Math

Calculus

Application Of Derivatives

If p and q are positive real numbers such that $p_{2}+q_{2}=1$, then the maximum value of $(p+q)$ is

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Find the point on the curve $9y_{2}=x_{3},$where the normal to the curve makes equal intercepts on the axes.

If length of three sides of a trapezium other than base are equal to 10cm, then find the area of the trapezium when it is maximum.

A cylindrica container is to be made from certain solid material with the following constraints: It has a fixed inner volume of $Vm_{3}$, has a 2 mm thick solid wall and is open at the top. The bottom of the container is a solid circular disc of thickness 2mm and is of radius equal to the outer radius of the container. If the volume the material used to make the container is minimum when the inner radius of the container is $10mm$. then the value of $250πV $ is

e total number of local maxima and local minima of the function $f(x)={(2+x)_{3},−3<x≤−1andx_{3},−1<x<2$ is

Find the equation of the tangent to the curve $y=3x−2 $which is parallel to the line $4x−2y+5=0.$

Using differentials, find the approximate value of $f(2.01),$where $f(x)=4x_{3}+5x_{2}+2.$

If the sum of lengths of hypotenuse and a side of a right angled triangle is given, show that area of triangle is maximum, when the angle between them is $3π ˙$

If $f(x)=x_{23}(3x−10),x≥0,$then $f(x)$is increasing in ____.