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Last updated date: 01st Dec 2023
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Statement I-Geometrically, derivative of a function is the slope of the tangent to the corresponding curve at a point.Statement II- Geometrically, indefinite integral of a function represents a family of curves parallel to each other.a)Statement I is true; statement II is true; statement II is a correct explanation for statement I.b)Statement I is true; statement II is true; statement II is not a correct explanation for statement I.c)Statement I is true; statement II is false.d)Statement I is false; statement II is true.

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Hint: Derivation of function of variable x which is the rate at the value of function changes with respect to the change of variable. Integration is a method of finding the area to the x axis from the curve.

Let there is a curve, $y = f\left( x \right)$
Slope of the tangent $= \tan \theta$ $= \dfrac{{dy}}{{dx}}$ at (x,y)
$\int {\dfrac{{df\left( x \right)}}{{dx}}dx = f\left( x \right)} + C$