minimum value of a cubic?? (1 Viewer)

[Masaken]

i know that to find minimum of a parabola if there is one is to use the vertex formula, but is there a general way to find the minimum value of a cubic or any graph in general??

View attachment 36126
(above is the qn i'm stuck on but i want to know how to do it on my own)

 

[Scimat]

You can differentiate to find stationary points and see which point gives you a minimum. But for cubic or most odd functions, they have no range restrictions. So they can take all values of y and thus have no minimum points

 

[Deem_Skills]

Ye use first derivative and let it equal 0 to get stationary points then get the double derivative and test those points to determine if it's concave up or down (if double derivative > 0 it's concave up and you have a minimum and if it's < 0 it's concave down and you have a maximum and if it's = 0 it's a horizontal point of inflexion and is not a max or min)

also beware that first derivative doesnt pick up on tips like in absolute value

 

[Masaken]

You can differentiate to find stationary points and see which point gives you a minimum. But for cubic or most odd functions, they have no range restrictions. So they can take all values of y and thus have no minimum points

Ye use first derivative and let it equal 0 to get stationary points then get the double derivative and test those points to determine if it's concave up or down (if double derivative > 0 it's concave up and you have a minimum and if it's < 0 it's concave down and you have a maximum and if it's = 0 it's a horizontal point of inflexion and is not a max or min)

also beware that first derivative doesnt pick up on tips like in absolute value

ohhhh, i forgot about using this, tyvm!!
(iirc this is a y12 topic right? would it still be fine to use it in a y11 yearly paper?)

 

[Deem_Skills]

ohhhh, i forgot about using this, tyvm!!
(iirc this is a y12 topic right? would it still be fine to use it in a y11 yearly paper?)

I doubt a question that requires that technique would appear in y11 because yes it's a year 12 topic. If I were you I'd make sure that there isnt any other way to solve the question and I'd go to it as a last resort otherwise it's probably not a good idea to use it unless the paper is for accelerated.