What are the approximate values of the minimum and maximum points of f(x) = x5 − 10x3 + 9x on [-3,3]?

Critical points: (Maximum, minimum, and inflection points) have a slope = 0
The derivative gives the slope, take the derivative set it equal to zero

f(x) = x^5 -10x^3 + 9x
derivative:
f'(x) = 5x^4 - 30x^2 + 9
0 = 5x^4 - 30x^2 + 9
use quadratic formula (or polysolver) with a=5, b=-30 and c = 9
4th degree gives 4 solutions

x = +/- √(3 - 6/√(5))
x ~ +/- 2.38

x = +/- √(3 - 6/√(5))
x ~ +/- 0.563

Determine which point is the highest (maximum) and the lowest (minimum) by putting the x-coordinates back into the original equation and comparing y-values.

 * You will also need to check the endpoints given as these can sometime be the max/min of the function.

Our x-values:
x = { -3, -2.38, -0.563, 0.563, 2.38, 3}

respective y-values found by inputting x's into function
y = {0, 37.03, -3.34, 3.34, -37.03, 0}

nice symmetry.. check out the graph to see the solutions are correct.
https://www.desmos.com/calculator

Maximum point (-2.38, 37.03)
Minimum point (2.38, -37.03)