class 12

Math

Calculus

Application of Derivatives

The function $f(x)=tan_{−1}(sinx+cosx)$is an increasing function in

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

Find the total number of parallel tangents of $f_{1}(x)=x_{2}−x+1andf_{2}(x)=x_{3}−x_{2}−2x+1.$

A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the maximum length of the hypotenuse is $(a_{32}+b_{32})_{23}$ .

The curve $f(x)=x−10x_{2}+ax+6 $ has a stationary point at $(4,1)$ . Find the values of $aandb$ . Also, show that $f(x)$ has point of maxima at this point.

A figure is bounded by the curves $y=x_{2}+1,y=0,x=0,andx=1.$ At what point $(a,b)$ should a tangent be drawn to curve $y=x_{2}+1$ for it to cut off a trapezium of greatest area from the figure?

Discuss the global maxima and global minima of $f(x)=tan_{−1}(g)_{e}x$ in$[3 1 ,3 ]$

Let $C$ be a curve defined by $y=e_{a}+bx_{2}˙$ The curve $C$ passes through the point $P(1,1)$ and the slope of the tangent at $P$ is $(−2)˙$ Then the value of $2a−3b$ is_____.

Find the locus of point on the curve $y_{2}=4a(x+as∈ax )$ where tangents are parallel to the axis of $x˙$

If the sub-normal at any point on $y=a_{1−n}x_{n}$ is of constant length, then find the value of $n˙$