my equation is y=0.5xcubed + 2xsquared+1xto the 4th. i know how to find the y intercepts but i cant remember how to find the x intercept. and i need help finding the max and min because i think i did it wrong

Question

anonymous · Answer

how did you do it?

anonymous · Answer

$$y = 0.5x^3 + 2x^2 + x^4$$

turingtest · Answer

x intercept is when y=0
$$y=0.5x^3+2x^2+x^4=0=x^2(0.5x+2x^2+1)$$

turingtest · Answer

$$=0.5x^2(4x^2+x+2)$$
so y-int =0 and whatever the solutions to that quadratic are
2x^2+0.5x+1=0

turingtest · Answer

max/min are when the derivative f'(x)=0, so$$y'=1.5x^2+4x+4x^3=x(x^3+1.5x+4)=0$$