Home › ISC Class 12 › Mathematics › Application of Derivatives › For $f(x)=2x^3-15x^2+36x+1$ on $[1,5]$, the abso…
For $f(x)=2x^3-15x^2+36x+1$ on $[1,5]$, the absolute minimum value is
A$28$
B$29$
C$24$
D$1$
Answer & Solution
Correct answer: C. $24$
1. Critical points from $f'(x)=6(x-2)(x-3)$ are $x=2,3$.
2. Values: $f(1)=24$, $f(2)=29$, $f(3)=28$, $f(5)=56$.
3. The smallest is $24$ at the endpoint $x=1$.
4. Trap $1$ is the constant term, not a computed value.
_Source: NCERT Class 12 Mathematics Ch 6 "Application of Derivatives", p.26_
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