Maths

Find the values of x for which f(x) is an increasing function, given that f(x)=5x^3+12x

That answer is that x belongs to real numbers.

I dont understand how you do this question. Ive found the derivative but i dont know what to do next

If the function is increasing, we have that $f'(x) \geq 0$.

So you want to solve the inequality $f'(x) \geq 0$.

Thank ypu very much for the reply. I tried to do that amd i couldnt solve it. Id really appreciate it if you solved it for me.

If the function is increasing, we have that $f'(x) \geq 0$.

So you want to solve the inequality $f'(x) \geq 0$.

Hi, just passing by. Would you need to find the second derivative of the equation to answer this?

Typically, I like to draw a brief sketch of the curve itself to get an idea of what I'm expecting to get. :P

Nope, you don't need the second derivative here.

i think i get it now. Is the answer because all values for x^2 are positive?

Nope, you don't need the second derivative here.

Oh shoot, wait. Yeah I got it. Didn't notice that the equation passed through (0,0). ^^

Yep, and from there you can quite simply show how $5x^2 + 4 \geq 0$ must be true for all $x \in \mathbb{R}$.

Cool, but I don't see why (0,0) is significant to you here. It shouldn't be