WP 34S problem in solving f'(x)=0

[lrdheat]

Calculus book example function (x^2 * (x+1)^3)/((x-2)^2 * (x-4)^4).

Trying to solve f'(x)=0 proves difficult. It really requires a close narrow interval to try solve with. Using an interval as narrow as 2.4 to 2.6 produces error +inf (correct answer is ~2.46675). Keep in mind that f(x) is continuous x>2 to x<4. Using a narrower solve interval of 2.46 to 2.48 produces an inaccurate answer of ~2.4774. Using an interval of 2.44 to 2.47 is even worse, producing a zero at a nonsensical 4.0002. Even using 2.466 to 2.467 gives the 2.4774 result.

The TI 36X Pro, by contrast quickly produces a much more accurate result using single guesses such as 2.1 or 3.9.

The Prime agrees with the TI answer to 5 decimal points.

Any ideas?