I can see the image you uploaded contains a set of math exercises written in Indonesian. Let me break down the tasks and provide a solution for the first one:

1. Tentukan titik-titik kritis dari fungsi dan interval berikut ini:

• a. $f(x) = x^3 + x^2 - x + 2$, $I = [-2,1]$
• b. $f(x) = |x| (x + 1)^2$, $I = [-1,1]$
• c. $f(x) = |x| (x^2 - 1)$, $I = [-1,1]$

Step-by-Step Solution for Part (a):

Function: $f(x) = x^3 + x^2 - x + 2$
Interval: $I = [-2, 1]$

1. Find the derivative:
   $f'(x) = 3x^2 + 2x - 1$

2. Find critical points by setting $f'(x) = 0$:
   Solve $3x^2 + 2x - 1 = 0$.

   The quadratic equation can be solved using the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ Here, $a = 3$, $b = 2$, and $c = -1$, so: $x = \frac{-2 \pm \sqrt{(2)^2 - 4(3)(-1)}}{2(3)} = \frac{-2 \pm \sqrt{4 + 12}}{6} = \frac{-2 \pm \sqrt{16}}{6} = \frac{-2 \pm 4}{6}$ The two solutions are: $x_1 = \frac{-2 + 4}{6} = \frac{2}{6} = \frac{1}{3}, \quad x_2 = \frac{-2 - 4}{6} = \frac{-6}{6} = -1$

3. Check if the critical points are in the interval $[-2,1]$:
   Both $x = \frac{1}{3}$ and $x = -1$ are in the interval $[-2,1]$.

4. Conclusion:
   The critical points are $x = -1$ and $x = \frac{1}{3}$.

Would you like me to continue with the rest of the parts (b and c) or further explain this part in more detail? Let me know if you have any questions!

Follow-up Questions:

1. How do we classify critical points as maxima or minima?
2. Can critical points exist outside the given interval?
3. How would we find the maximum or minimum values from the critical points?
4. What happens when we differentiate an absolute value function like in part (b)?
5. How can we check the concavity of functions at critical points?

Tip:

When solving quadratic equations in calculus, always double-check if the roots lie within the interval of interest.