If f(x)=x²+g^()(1) x+g^()(2) and g(x)=f(1) x²+x f^()(x)+f^()(x), then the value of f(4)-g(4) is equal to _ _ _ _ _ _.

Limit, Continuity and Differentiability: JEE Main 2023 Mathematics question

JEE Main 2023 · 1 Feb, Morning shift · Q31

JEE Main 20231 Feb, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

f(x)=x^{2}+g^{\prime}(1) x+g^{\prime \prime}(2)

and

g(x)=f(1) x^{2}+x f^{\prime}(x)+f^{\prime \prime}(x)

, then the value of

f(4)-g(4)

is equal to ____________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2023 · 1 Feb, Morning shift · Q31

JEE Main 20231 Feb, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

f(x)=x^{2}+g^{\prime}(1) x+g^{\prime \prime}(2)

and

g(x)=f(1) x^{2}+x f^{\prime}(x)+f^{\prime \prime}(x)

, then the value of

f(4)-g(4)

is equal to ____________.

Your answerType your answer. Integers and decimals are accepted.