class 12

Math

Calculus

Application of Derivatives

If $y_{2}=4b(x−c)$ and $y_{2}=8ax$ having common normal then $(a,b,c)$ is (A) $(21 ,2,0)$ (B) $(1,1,3)$ (C) $(1,1,1)$ (D) $(1,3,2)$

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An edge of a variable cube is increasing at the rate of 3 cm/s. How fast is the volume of the cube increasing when the edge is 10 cm long?

The slope of the normal to the curve $y=2x_{2}+3$sin x at $x=0$is(A) 3 (B) $31 $ (C)$−3$ (D) $−31 $

Show that $y=g(1+x)−2+x2x ,x≻1$, is an increasing function of x throughout its domain.

Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals:(i) $f(x)=x_{2},x∈[−2,2]$ (ii) $f(x)=sinx+cosx,x∈[0,π]$(iii) $f(x)=4x−21 x_{2},x∈[−2,29 ]$ (iv) f(x)=(x-1)

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

Find the intervals in which the following functions are strictly increasing or decreasing:(a) $x_{2}+2x−5$ (b) $10−6x−2x_{2}$ (c) $−2x_{3}−9x_{2}−12x+1$ (d) $6−9x−x_{2}$(e) $(x+1)_{3}(x−3)_{3}$

A stone is dropped into a quiet lake and waves move in circles at a speed of 4cm per second. At the instant, when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing?

Find points on the curve $9x_{2} +16y_{2} =1$at which the tangents are(i) parallel to x-axis (ii) parallel to y-axis.