Analyze the given function using calculus f(x)=(1/x)+ln(x)

Question

Analyze the given function using calculus f(x)=(1/x)+ln(x)

a. Identify all local extrema.

b. Identify the x-intercept and y-intercepts of the function.

c. Is the function symmetric about the x-axis, y-axis, or origin?

d. State the domain of the function.

Answer 1

d) Domain: x > 0

b) No y-intercept because x = 0 not in domain. x- intercept: y = 1/x + lnx = 0; no solution, no x-intercept

c) no any symmetry

a) f'(x) = - 1/x² + 1/x = 0; - 1 + ,x = 0, x = 1

f''(x) = 2/x³ - 1/x²; f''(1) = 1 > 0. So, at x = 1 f(x) has local minimum: f(1) = 1