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 maximum value is
A$29$
B$56$
C$28$
D$24$
Answer & Solution
Correct answer: B. $56$
1. $f'(x)=6x^2-30x+36=6(x-2)(x-3)$, critical points $x=2,3$.
2. Evaluate at critical points and endpoints: $f(1)=24$, $f(2)=29$, $f(3)=28$, $f(5)=56$.
3. The largest value is $56$ at $x=5$.
4. Trap $29$ is only the local-maximum value, not the absolute maximum.
_Source: NCERT Class 12 Mathematics Ch 6 "Application of Derivatives", p.26_
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