Let f(x)=5x^4-12x^3 a) find The x-coordinates of all critical points of f. B) fi

Question

Let f(x)=5x^4-12x^3 a) find The x-coordinates of all critical points of f. B) find intervals of increase and intervals if decrease c) at which value of x have local max and mim Let f(x)=5x^4-12x^3 a) find The x-coordinates of all critical points of f. B) find intervals of increase and intervals if decrease c) at which value of x have local max and mim Let f(x)=5x^4-12x^3 a) find The x-coordinates of all critical points of f. B) find intervals of increase and intervals if decrease c) at which value of x have local max and mim

Explanation / Answer

f(x)=5x4-12x3

f '(x)=20x3-36x2

a) for critical points f '(x)=0

==>4x2(5x-9)=0

=>.x=0,x=9/5

b) function increasing ==> f '(x)>0

==>20x3-36x2>0

==>x=(9/5, infinity)

function decreasing ==> f '(x)<0

==>20x3-36x2<0

==>x=(-infinity,9/5)

c) for x<0 , f '(x)<0, for 0<x<9/5 ,f '(x) <0 ==> x=0 is not a local maximum or minimum

for x<9/5 , f '(x)<0, for x>9/5 ,f '(x) >0 ==> x=9/5 is a local minimum

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