4. • Question Details Consider the following function. F(x) - In(7 - In x) (a) F

Question

4. • Question Details Consider the following function. F(x) - In(7 - In x) (a) Find the critical numbers of f. (Enter your answers as a comma-separated list.) (b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) increasing decreasing (c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.) relative maximum (x, y)-( relative minimum (x, y) = ( Submit Answer Save Progress

Explanation / Answer

a)

f(x) = ln(7-lnx)

f'(x) = 1/(7-lnx) *(0-1/x)

f'(x) = 1/(x*(lnx -7))

To find critical point, set f'(x) = 0 and then solve for x

1/(x*(lnx -7)) =0

x = No solution.

hence no critical point

x=DNE

b)

Increaseing when f'(x)>0, hence

DNE

Decreasing when f'(x)<0, hence

(0, e7)

c)

Relative maximum : DNE

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