Question

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

Answer 1

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

Answer 2

its a simple polynomial; the rules are very basic

Answer 3

Cx^n becomes (C*n) x^(n-1)

Answer 4

3x^5 becomes (3*5) x^(3-1); 15x^4

Answer 5

concave up if f''[x]>0 and concave down if f''[x]<0, inflection point at f''[x]=0

Answer 6

test for etrema by setting f'[x]=0 or f''[x]=0

Answer 7

basically solve \[15x^4-20x^3=0\]

Answer 8

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

Answer 9

thanks for the help. i was also wondering to find where the function is increasing or decreasing, do i use the critical point?