Question

find the extreme point(s) of the function f(x) = 0.25x^4 + 3x^3 - 18x^2 +10 and classify them

Answer 1

what do you mean by extreme points?

Answer 2

i think they mean extrema, maxima and minima, correct?

Answer 3

most likely, in that case differentiate and set equal to zero

Answer 4

differentiate the equation. then use fishball method

Answer 5

f(x) = \[0.25x^4 + 3x^3 - 18x^2 +10\]
Then differentiate f'(x) = \[x^3 + 9x^2 - 36x\]=
\[x(x^2 + 9x - 36)\]=
\[x(x+12)(x-3)\]

Answer 6

Then use fishball method
-12 0 3
x - - - 0 + + +
x+12 - 0 + + + + +
x-3 - - - - - 0 +
--------------------------------
- 0 + 0 - 0 +
therefore, at x=-12 and x=3 there exists rel. min
at x = 0, there exists rel max

Hope I helped and I hope I did it right

Answer 7

yes i believe this is correct

Answer 8

Oh gosh thanks so much you guys this really helps