Originally Posted by

**11rdc11** Hi guys for some reason I'm having problems with these 2 questions, Any help would be great.

1. For the equation $\displaystyle 60x^3-3x^5 = y$ where does the largest slope occur?

Ok here is how I thought I would find the answer for this problem. If I take the second derivative and equal it to 0 and find my critical points, then one of my points will be the the largest slope. Is this correct?

$\displaystyle f(x) = 60x^3-3x^5$

$\displaystyle f'(x) = 180x^2 -15x^4$

$\displaystyle f''(x) = 360x -60x^3$

so

$\displaystyle 0 = 60x(6-x^2)$

so

$\displaystyle x = 0, \sqrt{6}, -\sqrt{6}$

so I think my largest slope occurs at

$\displaystyle \sqrt{6}, -\sqrt{6}$

Is this correct?