Class 12

Math

Calculus

Application of Derivatives

The normal at the point (1,1) on the curve $2y+x_{2}=3$is(A) $x+y=0$ (B) $xy=0$ (C) $x+y+1=0$(D) $xy=0$

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Find the point on the curve $y=x_{3}−11x+5$ at which the tangent is $y=x−11.$

Find the point on the curve $y_{2}=4x$ which is nearest to the point $(2,−8)$.

A balloon, which always remains spherical on inflation, is being inflated by pumping in $900$ cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is $15cm$.

Find a point on the curve $y=(x−2)_{2}$ at which the tangent is parallel to the chord joining the points $(2,0)$ and $(4,4)$.

Verify Lagranges's mean-value theorem for the following function:$f(x)=tan_{−1}x$ on $[0,1]$

The total revenue in Rupees received from the sale of $x$ units of a product is given by $R(x)=3x_{2}+36x+5$. The marginal revenue, when $x=15$ is.

Using differentials, find the sum of digits approximate value of the following up to $3$ places of decimal.$(0.999)_{101}$

An edge of a variable cube is increasing at the rate of $5cm/s$. How fast is the volume of the cube increasing when the edge is $10cm$ long?