Mathematics · JEE

Important Questions: Derivatives of order upto two for JEE

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Q1MathsUnit 7: Limit, Continuity and Differentiability

Assertion(A): Let

\boldsymbol{f}(\boldsymbol{x})

be twice differentiable function such that

\boldsymbol{f}^{\prime \prime}(\boldsymbol{x})=-\boldsymbol{f}(\boldsymbol{x})

and

\boldsymbol{f}^{\prime}(\boldsymbol{x})=\boldsymbol{g}(\boldsymbol{x}) .

\boldsymbol{h}(\boldsymbol{x})=[\boldsymbol{f}(\boldsymbol{x})]^{2}+[\boldsymbol{g}(\boldsymbol{x})]^{2}

and

\boldsymbol{h}(\mathbf{1})=\mathbf{8}

\operatorname{then} h(2)=8

Reason (R): Derivative of a constant function is zero.

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