75. b. Identify the function’s local and absolute extreme values, if any, saying where they occur.
g(x) = x(ln x)²

Find the exact length of the curve $y=\ln (\sec (x\left)\right)$ for $0\le x\le \frac{\pi }{6}$.

Which of the following points is a location where the function $f\left(x\right)=\frac{1}{x-2}$ is discontinuous?

Log-normal probability distribution A commonly used distribution in probability and statistics is the log-normal distribution. (If the logarithm of a variable has a normal distribution, then the variable itself has a log-normal distribution.) The distribution function is

f(x) = 1/xσ√(2π) e⁻ˡⁿ^² ˣ / ²σ^², for x ≥ 0

where ln x has zero mean and standard deviation σ > 0.

e. For what value of σ > 0 in part (d) does ƒ(x*) have a minimum?

71. Locate and identify the absolute extreme values of cos(ln x) on [1/2, 2]

Find the critical points of the given function.

$g(x)=\frac13x^3-\frac12x^2-12x$

Find the critical points of the given function.

$f(t)=\frac{6t}{t^2+1}$

Find the critical points of the given function.

$f(x)=\sqrt{2-x^2}$

Find the global maximum and minimum values of the function on the given interval. State as ordered pairs.

$y=x+\frac{2}{x};[0.25,3]$