Class 12

Math

Calculus

Application of Derivatives

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

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

The length $x$ of a rectangle is decreasing at the rate of $5cmm $ and the width $y$ is increasing at the rate of $4cmm $ When $x=8cm$ and $y=6cm,$ find the rate of change of (a) the perimeter and (b) the area of the rectangle.

If the function $y=f(x)$ is represented as $x=ϕ(t)=t_{5}−5t_{3}−20t+7$, $y=ψ(t)=4t_{3}−3t_{2}−18t+3(∣t∣<2),$ then find the maximum and minimum values of $y=f(x)˙$

The tangent at any point on the curve $x=acos_{3}θ,y=asin_{3}θ$ meets the axes in $PandQ$ . Prove that the locus of the midpoint of $PQ$ is a circle.

An electric light is placed directly over the centre of a circular plot of lawn 100 m in diameter. Assuming that the intensity of light varies directly as the sine of the angle at which it strikes an illuminated surface and inversely as the square of its distance from its surface, how should the light be hung in order that the intensity may be as great as possible at the circumference of the plot?

Find the maximum value and the minimum value and the minimum value of $3x_{4}−8x_{3}+12x_{2}−48x+25$ on the interval $[0,3]˙$

A curve is given by the equations $x=sec_{2}θ,y=cotθ˙$ If the tangent at $Pwhereθ=4π $ meets the curve again at $Q,then[PQ]$ is, where [.] represents the greatest integer function, _________.

Find the angle of intersection of $y=a_{x}andy=b_{x}$

A curve is defined parametrically be equations $x=t_{2}andy=t_{3}$ . A variable pair of perpendicular lines through the origin $O$ meet the curve of $PandQ$ . If the locus of the point of intersection of the tangents at $PandQ$ is $ay_{2}=bx−1,$ then the value of $(a+b)$ is____