Question:medium
If $f(x)=2x^{3}-3x^{2}-\lambda x+1, x\in[0,3]$ attains a local minimum at $x=2$, then the value of $\lambda$ is equal to
If $f(x)=2x^{3}-3x^{2}-\lambda x+1, x\in[0,3]$ attains a local minimum at $x=2$, then the value of $\lambda$ is equal to
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Logic Tip: Extrema always occur at critical points where $f'(x) = 0$. The moment you see "local minimum at $x=c$", immediately write down $f'(c) = 0$ to set up your primary equation.
Updated On: Apr 27, 2026
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The Correct Option is C
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