Class 12

Math

Calculus

Application of Derivatives

Find all the points of local maxima and local minima of the function f given by $f(x)=2x_{3}−6x_{2}+6x+5$

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

Discuss the extremum of $f(x)=31 (x+x1 )$

If the radius of a sphere is measured as 9cm with an error of 0.03 cm, then find the approximate error in calculating its volume.

If in a triangle $ABC,$ the side $c$ and the angle $C$ remain constant, while the remaining elements are changed slightly, show that $cosAda +cosBdb =0.$

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?

If the tangent at $(1,1)$ on $y_{2}=x(2−x)_{2}$ meets the curve again at $P,$ then find coordinates of $P˙$

How many roots of the equation \displaystyle{\left({x}-{1}\right)}{\left({x}-{2}\right)}{\left({x}-{3}\right)}+{\left({x}-{1}\right)}{\left({x}-{2}\right)}{\left({x}-{4}\right)}+{\left({x}-{2}\right)}{\left({x}-{3}\right)}{\left({x}-{4}\right)}+{\left({x}-{1}\right)}{\left({x}-{3}\right)}{\left({x}-{4}\right)}={0} are positive?

Find the values of $a$ if equation $1−cosx=23 ∣x∣+a,x∈(0,π),$ has exactly one solution.

If $f(x)andg(x)$ are continuous functions in $[a,b]$ and are differentiable in$(a,b)$ then prove that there exists at least one $c∈(a,b)$ for which. $∣f(a)f(b)g(a)g(b)∣=(b−a)∣∣ f(a)f_{prime}(c)g(a)g_{prime}(c)∣∣ ,wherea<c<b˙$