Limit, Continuity and Differentiability: JEE Main 2020 Mathematics question

JEE Main 2020 · 4 Sep, Morning shift · Q28

JEE Main 20204 Sep, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Suppose a differentiable function f(x) satisfies the identity f(x+y) = f(x) + f(y) + xy² + x²y, for all real x and y.

\mathop {\lim }\limits_{x \to 0} {{f\left( x \right)} \over x} = 1

, then f'(3) is equal to ______.

Your answerType your answer. Integers and decimals are accepted.

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JEE Main 2020 Limit, Continuity and Differentiability Question with Answer (4 Sep Morning shift, Q28) | JEE Arc

JEE Main 2020 · 4 Sep, Morning shift · Q28

JEE Main 20204 Sep, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Suppose a differentiable function f(x) satisfies the identity f(x+y) = f(x) + f(y) + xy² + x²y, for all real x and y.

\mathop {\lim }\limits_{x \to 0} {{f\left( x \right)} \over x} = 1

, then f'(3) is equal to ______.

Your answerType your answer. Integers and decimals are accepted.