Please show all stepsSolutionfx 2x5 35x4 80 x3 f x 10x4

Please show all steps.

Solution

f(x) = -2x^5 + 35x^4 - 80 x^3

f \' (x) = -10x^4 + 140x^3 - 240x^2 = 0

=> x^4 - 14x^3 + 24x^2 = 0

=> x^2 ( x^2 - 14 x + 24 ) =0

=> x^2 (x^2 - 12x -2x + 24) =0

=> x^2 (x(x-12) - 2(x -12)) =0

=> x^2 (x-12)(x-2) =0

x = 0 , 2 , 12

Critical Points : 0 ,2 ,12 Answer

Intervals:

(-infinity , 0) : Increasing

(0,2) : Increasing

(2 ,12) : Decreasing

(12 , + infinity) : Increasing

Therefore,

x =0 : Neither Maximum nor minumum

x =2 : Relative Maximum

x =12 : Relative Mininum