Show that f(x) = x^9 + 4x^7 + 11 is an increasing function for al… - Vidyadip

Question

Show that $f(x) = x^9 + 4x^7 + 11$ is an increasing function for all $\text{x}\in\text{R}.$.

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Answer

$f(x) = x^9 + 4x^7 + 11$
$f'(x) = 9x^8 + 28x^6$
$= x^6(9x^2 + 28)$
Now,
$\text{x}\in\text{R}$
$\Rightarrow x^6 > 0$ and $9x^2 + 28 > 0$
$\Rightarrow x^6(9x^2 + 28) > 0$
$\Rightarrow f'(x) > 0$
So, $f(x)$ is increasing on function for $\text{x}\in\text{R}.$

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