How to Find Critical Points of f(x) = xln(x)

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SUMMARY

The critical points of the function f(x) = xln(x) are determined by setting its derivative f'(x) = ln(x) + 1 to zero. The correct derivative is f'(x) = ln(x) + 1, not ln(x) + x. To find the critical points algebraically, solve the equation ln(x) + 1 = 0, which simplifies to x = e^(-1). This indicates that the critical point occurs at x = 1/e.

PREREQUISITES
  • Understanding of calculus, specifically differentiation
  • Familiarity with logarithmic functions
  • Knowledge of algebraic manipulation
  • Experience with solving equations involving natural logarithms
NEXT STEPS
  • Study the properties of logarithmic functions and their derivatives
  • Learn how to solve equations involving natural logarithms
  • Explore the concept of critical points and their significance in calculus
  • Practice finding critical points for various functions using algebraic methods
USEFUL FOR

Students studying calculus, mathematics educators, and anyone seeking to deepen their understanding of critical points in functions involving logarithms.

jtulloss
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I need help finding the critical points of this equation:

f(x) = xln(x)

I found f'(x) to be ln(x)+x, but I don't know how to solve for x when setting f'(x) to 0 to find the critical points. I know I can find the zeros of f'(x) graphically on a calculator, but I need to know how to do it algebraically.

Thanks.
 
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jtulloss said:
I need help finding the critical points of this equation:

f(x) = xln(x)

I found f'(x) to be ln(x)+x,
It's not lnx + x.
 
Ah man, I can't believe I overlooked that. I've been doing that a lot lately with studying for exams and all. I got it now.

Thanks
 

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