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anonymous

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    function is decreasing if f'[x] <0 (negative) for open interval function increasing if f'[x}>0 (positive) for open interval \[f'[x] = 15x^4-20x^3\]

  2. amistre64
    • 5 years ago
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    its a simple polynomial; the rules are very basic

  3. amistre64
    • 5 years ago
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    Cx^n becomes (C*n) x^(n-1)

  4. amistre64
    • 5 years ago
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    3x^5 becomes (3*5) x^(3-1); 15x^4

  5. anonymous
    • 5 years ago
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    concave up if f''[x]>0 and concave down if f''[x]<0, inflection point at f''[x]=0

  6. anonymous
    • 5 years ago
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    test for etrema by setting f'[x]=0 or f''[x]=0

  7. anonymous
    • 5 years ago
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    basically solve \[15x^4-20x^3=0\]

  8. anonymous
    • 5 years ago
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    or http://www.wolframalpha.com/input/?i=extrema++f%28x%29%3D3x^5+-+5^4+%2B1

  9. anonymous
    • 5 years ago
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    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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