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STD 12 - 6. Application of derivatives — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 6. Application of derivatives4 Marks
Question
Given $\lambda \in [0,20]$, then number of integral values of $\lambda$ for which the function $f(x) = x^3 -12x + \lambda$ has a point of maxima-
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Answer

d
$\because f(\mathrm{x})=\mathrm{x}^{3}-12 \mathrm{x}+\lambda \Rightarrow f^{\prime}(\mathrm{x})=3(\mathrm{x}-2)(\mathrm{x}+2)$

clearly $f(\mathrm{x})$ is maximum at $\mathrm{x}=-2 \forall \lambda \in[0,20]$

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