class 12

Math

Calculus

Application of Derivatives

Twenty metres of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in $sqm˙)$of the flower-bed is: 25 (2) 30 (3) 12.5 (4) 10

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The line $y=x+1$is a tangent to the curve $y_{2}=4x$at the point(A) $(1,2)$ (B)$(2,1)$ (C) $(1,2)$ (D) $(1,2)$

Find the approximate change in the volume V of a cube of side x meters caused by increasing the side by 2%.

A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening.

Prove that the function f given by $f(x)=x_{2}−x+1$is neither strictly increasing nor strictly decreasing on $(1,1)$.

Find points at which the tangent to the curve $y=x_{3}−3x_{2}−9x+7$is parallel to the x-axis.

Prove that the logarithmic function is strictly increasing on $(0,∞)$.

Find points on the curve $4x_{2} +25y_{2} =1$at which the tangents are (i) parallel to x-axis (ii) parallel to y-axis.

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