Let $f(x)=a x^3+b x^2+c x+41$ be such that $f(1)=40, f^{\prime}(1)=2$ and $f^{\prime \prime}(1)=4$. Then $a ^2+ b ^2+ c ^2$ is equal to : [JEE Main 2024, 9 Apr (Shift 1)]

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Let \(f(x)=a x^3+b x^2+c x+41\) be such that \(f(1)=40, f^{\prime}(1)=2\) and \(f^{\prime \prime}(1)=4\). Then \(a ^2+ b…

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