Class 12

Math

Calculus

Application of Derivatives

Using differentials, find the approximate value of $(3.968)_{23}$

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Find the slope of the tangent to the curve $y=x_{3}−3x+2$ at the point whose x-coordinate is 3.

A wire of length 28 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum?

) Find the intervals in which the function $sin3x,x∈[0,2π ]$, is (a) increasing (b) decreasing

Find the equations of the tangent and normal to the parabola $y_{2}=4ax$at the point $(at_{2},2at)$.

Find the least value of a such that the function f given by $f(x)=x_{2}+ax+1$is strictly increasing on $(1,2)˙$

Find the points on the curve $x_{2}+y_{2}−2x−3=0$at which the tangents are parallel to the x-axis.

Manufacturer can sell x items at a price of rupees $(5−100x )$each. The cost price of x items is Rs $(5x +500)$. Find the number of items he should sell to earn maximum profit

Find absolute maximum and minimum values of a function f given by $f(x)=12x_{34}−6x_{31},x∈[−1,1]$.