Show that f(x) = x^3 - 15x^2 + 75x - 50 is an increasing function… - Vidyadip

Question

Show that $f(x) = x^3 - 15x^2 + 75x - 50$ is an increasing function for all $\text{x}\in\text{R}.$

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Answer

$f(x) = x^3 - 15x^2 + 75x - 50$
$f'(x) = 3x^2 - 30x + 75$
$= 3(x^2- 10x + 25)$
$=3(\text{x}-5)^2>0,\forall\ \text{x}\in\text{R}$ $[\because$ Square of any function is always greater than zero$]$
So, f(x) is an increasing function for all $\text{x}\in\text{R}.$

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