f(x)=ln(x^4+27) a. Find the interval on which f is increasing and decreasing. b. Find the local minimum value of f c. Find the inflection points (2) d.Find the interval on which f is concave up...

f(x)=ln(x^4+27)

a. Find the interval on which f is increasing and decreasing.

b. Find the local minimum value of f

c. Find the inflection points (2)

d.Find the interval on which f is concave up and down

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a) You need to perform the first derivative test, hence you need to find f'(x) such that:

`f'(x) = (4x^3)/(x^4+27)`

You need to solve f'(x) = 0 such that:

`(4x^3)/(x^4+27) = 0 =gt 4x^3 = 0 =gt x = 0`

You need to select a value smaller than 0 such that:

`f'(-1) = -4/28 lt 0`

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