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Application of Derivatives
NCERT Class 12
CBSE
Grade 12
Question:
Find all the points of local maxima and local minima of the function $f(x) = 2x^3 - 6x^2 + 6x + 5$.
Step-by-Step Solution
$f'(x) = 6(x-1)^2 = 0 \Rightarrow x = 1$. [1.0 Mark] $f'(x) > 0$ on both sides of $x = 1$. [1.0 Mark] $x = 1$ is a point of inflection (no local max or min). [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Finding critical point $x=1$: 1.0 Mark Applying First Derivative Test: 1.0 Mark Concluding point of inflection: 1.0 Mark
Correct Answer:
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