CBSE Class 12 Math 2020 Outside Delhi Set 1 Solved Paper

Question : 14 of 36

Marks: +1, -0

The slope of the tangent to the curve

{\y}=x^3-x

at the point

(2,6)

is____________
OR
The rate of change of the area of a circle with respect to its radius

r

, when

{\r}=3 {\cm}

, is________

Solution:

y=x^3-x

\;{d y}/{d x}=3 x^2-1

\;\text " slope of tangent "\;=\;{d y}/{d x}

=3 x^2-1

x=2

\;\text " Slope of tangent "\;\;=3(2)^2-1

\;=12-1

\;=11

6 π {\cm}^2 \/ {\cm}

Explanation: Area of circle,

{\A}=π r^2

∴ \;\; \;{d {\A}}/{d r}\;=2 π r

{ [\;{d {\A}}/{d r}] _{r=3 {\cm}} }\;=2 × π × 3

\;=6 π {\cm}^2 \/ {\cm}

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