anonymous
  • anonymous
Can someone help me to find where the function is increasing and decreasing, find the extrema's and determine if the function is concave up or down? The equation is f(x)=3x^5 - 5^4 +1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
function is decreasing if f'[x] <0 (negative) for open interval function increasing if f'[x}>0 (positive) for open interval \[f'[x] = 15x^4-20x^3\]
amistre64
  • amistre64
its a simple polynomial; the rules are very basic
amistre64
  • amistre64
Cx^n becomes (C*n) x^(n-1)

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amistre64
  • amistre64
3x^5 becomes (3*5) x^(3-1); 15x^4
anonymous
  • anonymous
concave up if f''[x]>0 and concave down if f''[x]<0, inflection point at f''[x]=0
anonymous
  • anonymous
test for etrema by setting f'[x]=0 or f''[x]=0
anonymous
  • anonymous
basically solve \[15x^4-20x^3=0\]
anonymous
  • anonymous
or http://www.wolframalpha.com/input/?i=extrema++f%28x%29%3D3x^5+-+5^4+%2B1
anonymous
  • anonymous
thanks for the help. i was also wondering to find where the function is increasing or decreasing, do i use the critical point?

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