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y= f(x) is a polynomial function passing through point (0, 1) and which increases in the intervals (1, 2) and (3, oo) and decreases in the intervals (oo,1) and (2, 3). If f(1) = -8, then the value of f(2) is |
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Answer» -3 Hence, `f'(x)=a(x-1)(x-2)(x-3), a gt 0` `implies f(x)=int a(x^(3)-6x^(2)+11x-6)dx` `=a((x^(4))/(4)-2x^(3)+(11x^(2))/(2)-6x)+C` Also, `f(0)=1 implies c=1` ` :. f(x)=a((x^(4))/(4)-2x^(3)+(11x^(2))/(2)-6x)+1 "(1)" ` So, graph is symmetrical about line `x=2` and range is `[f(1), OO) or [f(3),oo).` `f(1)=8` `implies a(-(9)/(4))+1=-8` `impliesa=4` `:. f(2)= -7` |
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