Differentiation Question 3
Question 3 - 2024 (27 Jan Shift 1)
Let $f(x)=x^{3}+x^{2} f^{\prime}(1)+x f^{\prime \prime}(2)+f^{\prime \prime \prime}(3), x \in R$.
Then $f^{\prime}(10)$ is equal to
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Answer (202)
Solution
$$ \begin{aligned} & f(x)=x^{3}+x^{2} \cdot f^{\prime}(1)+x \cdot f^{\prime \prime}(2)+f^{\prime \prime \prime}(3) \\ & f^{\prime}(x)=3 x^{2}+2 x f^{\prime}(1)+f^{\prime \prime}(2) \\ & f^{\prime \prime}(x)=6 x+2 f^{\prime}(1) \\ & f^{\prime \prime \prime}(x)=6 \\ & f^{\prime}(1)=-5, f^{\prime \prime}(2)=2, f^{\prime \prime \prime}(3)=6 \\ & f(x)=x^{3}+x^{2} \cdot(-5)+x \cdot(2)+6 \\ & f^{\prime}(x)=3 x^{2}-10 x+2 \\ & f^{\prime}(10)=300-100+2=202 \end{aligned} $$
