Question

What are the critical values, if any, of `f(x)= (x-2)(x+5)(x-7)*lnx`?

Answer 1

They are approximately `1.452` and `5.136`.

Explanation:

`f(x) = (x^3-4x^2-31x+70)lnx`

Use the product rule to find

`f'(x)=(3x^2-8x-31)lnx + (x^2-4x-31+70/x)`

`f'(x)` is defined for all `x` in the domain of `f`.

So the critical value will be the solutions to

`(3x^2-8x-31)lnx + (x^2-4x-31+70/x) = 0`

Use whatever technology or approximation technique you have available to find that the solutions are approximately `1.452` and `5.136`.