Show that the function $f(x) = x^5 - 10x^3 + 50x - 21$ is an increasing function for all x values. I have worked out that $dy/dx = 5x^4 - 30x^2 + 50$ and this must be greater than $0$ if it is an increasing function.

I simplified this to $x^4 - 6x^2 + 10 &gt; 0$. I know that I must prove this inequality true but I cannot work out how.

I am able to input various values of x and show them to be larger than 0 but am unsure how to do it algebraically.

I know for a quadratic, I can put it into a 'complete the square' form and then you can prove it to be larger than 0 as squaring something = positive and then adding a positive will remain positive. But am unsure how to do it where power of x > 2.
Complete the square: $x^4-6x^2+10=(x^2-3)^2+1$
Let rewrite that function as
$$f(x)=(x^5+50x)-(10x^3+21)$$
Obviously,
$$(10x^3+21)&lt;(x^5+50x)$$
Hence, function is increasing :D