F(x)=x^(-2) lnx
I know u have to get the derivative first, so I got x^-2(x^-1)+lnx(-2x^-3) but after that idk what to do.
I know u have to get the derivative first, so I got x^-2(x^-1)+lnx(-2x^-3) but after that idk what to do.
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set the first derivative = 0
x^-2(x^-1)+lnx(-2x^-3) = 1/x^3 - ln(x)/(2x^3) Using positive exponents often makes it easier to solve for
This function is not defined at x = 0.
1/x^3 = ln(x) / (2x^3) Multiply by 2x^3
(2^3)(1/x^3) = 2
2 = ln (x) Use each side as an exponent of e
e^2 = e^(ln(x)) e and ln are inverse function and cancel each other out
e^2 = x This is your critical point
x^-2(x^-1)+lnx(-2x^-3) = 1/x^3 - ln(x)/(2x^3) Using positive exponents often makes it easier to solve for
This function is not defined at x = 0.
1/x^3 = ln(x) / (2x^3) Multiply by 2x^3
(2^3)(1/x^3) = 2
2 = ln (x) Use each side as an exponent of e
e^2 = e^(ln(x)) e and ln are inverse function and cancel each other out
e^2 = x This is your critical point