Practicing Success
Practicing Success
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Let f(x) be a function defined by $f(x)=\int_1^xx(x^2-3x+2)dx,\,1≤x≤3$. Then the range of f(x) is: |
[0, 2] $[-\frac{1}{4},4]$ $[-\frac{1}{4},2]$ None of these |
$[-\frac{1}{4},2]$ |
f'(x) = x(x - 1)(x - 2) $f(2)=-\frac{1}{4}$ f(3) = 2 f(1) = 0 $f_{min}=min[f(1),f(2),f(3)]=-\frac{1}{4}\,∀\, x∈[1,3]$ $f_{max}=max[f(1),f(3)]=2\,∀\, x∈[1,3]$; Range = $[-\frac{1}{4},2]$ |
