Find the critical numbers of the function.$\displaystyle f(x) = x^3 + x^2 - x$ whats the smaller value and the larger value? the derivative of this is 3x^2+2x-1 but i get lost right after.
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Originally Posted by break Find the critical numbers of the function.$\displaystyle f(x) = x3 + x2 - x$ whats the smaller value and the larger value? the derivative of this is 3x^2+2x-1 but i get lost right after. critical values occur where f'(x) = 0 or where f'(x) is undefined. set the above derivative equal to 0 and solve for the critical values of x, then determine extrema.
okay so $\displaystyle 3x^2+2x-1=0$ $\displaystyle 2x-1=3x^2$ $\displaystyle -1=3x^2/2x$ $\displaystyle -1=3x/2$ $\displaystyle 0 = (3x+2)/2$ then $\displaystyle 0 = 3x+2$ $\displaystyle -2/3 = x$ not sure if i got this part right.
Originally Posted by break Find the critical numbers of the function.$\displaystyle f(x) = x^3 + x^2 - x$ whats the smaller value and the larger value? the derivative of this is 3x^2+2x-1 but i get lost right after. f(x)=(x^3)+(x^2)-x f'(x)=(3x^2)+(2x)-1 set that equal to zero. you will have to factor the polynomial to get (3x-1)(x+1)=0 so 3x-1=0 3x=1 x=1/3 x+1=0 x=-1 those are your critical values
Originally Posted by skeeter critical values occur where f'(x) = 0 or where f'(x) is undefined. set the above derivative equal to 0 and solve for the critical values of x, then determine extrema. from my understanding, critical values are where f'(x)=0 partition numbers are where f'(x)=0 or is undefined
Originally Posted by propjohn from my understanding, critical values are where f'(x)=0 partition numbers are where f'(x)=0 or is undefined Pauls Online Notes : Calculus I - Critical Points
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