Civil Engineering > GATE 2022 SET-2 > Calculus
Consider the polynomial f(x)=x3-6x2+11x-6 on the domain S given by 1 ≤ x ≤ 3. The first and second derivatives are f'(x) and f''(x).
Consider the following statements:
I. The given polynomial is zero at the boundary points x=1 and x=3.
II. There exists one local maxima of f(x) within the domain S.
III. The second derivative f''(x)>0 throughout the domain S.
IV. There exists one local minima of f(x) within the domain S.
The correct option is:
Consider the following statements:
I. The given polynomial is zero at the boundary points x=1 and x=3.
II. There exists one local maxima of f(x) within the domain S.
III. The second derivative f''(x)>0 throughout the domain S.
IV. There exists one local minima of f(x) within the domain S.
The correct option is:
Correct : b
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