for the polynomial f(x) = x^4-3x^3-4x^2
find the x and y intercepts and determine the local maxima and minima if any exist, rounded to 3 decimal places

Question

for the polynomial f(x) = x^4-3x^3-4x^2
find the x and y  intercepts and determine the local maxima and minima if any exist, rounded to 3 decimal places

anonymous · Answer

To find the x-intercepts, let y = 0 and solve for x. To find the y-intercept, let x = 0 and solve for y. Then differentiate f with respect to x and set it to 0 and solve for x. If unsolvable, it means there's no local maxima or minima.

anonymous · Answer

so the y intercept would be 0 but I still do not understand how to find the x-intercept

anonymous · Answer

$$y = x^4 - 3x^3 - 4x^2$$$$x^4 - 3x^3 - 4x^2 = 0$$$$x^2(x^2 - 3x - 4) = 0$$$$x^2(x - 4)(x + 1) = 0$$So, the x-intercept are (4 , 0), (0 , 0) and (-1 , 0).

anonymous · Answer

what does that have to do in relation to the local maxima and minima?

anonymous · Answer

Do you know differentiation?

anonymous · Answer

no..

anonymous · Answer

Lol, I don't know any other method except graphing it and looking at the points or differentiation...

anonymous · Answer

okay, thank you!