Let's solve the problems one by one from the uploaded image. You want to find the first and second derivatives and the critical points for each function.

I will start with Problem 883 (a):

Given function:

$y = 2x^2 - 7x + 1$

Step 1: First derivative ($y'$):

$y' = \frac{d}{dx}(2x^2) - \frac{d}{dx}(7x) + \frac{d}{dx}(1)$ $y' = 4x - 7$

Step 2: Second derivative ($y''$):

$y'' = \frac{d}{dx}(4x) - \frac{d}{dx}(7)$ $y'' = 4$

Step 3: Critical points:

Critical points occur when $y' = 0$: $4x - 7 = 0$ $x = \frac{7}{4}$

The critical point is at $x = \frac{7}{4}$.

Would you like me to proceed with more parts (e.g., 883(b), 884, etc.), or explain a specific step in more detail? Let me know how you'd like to proceed!

Further Questions:

1. What are critical points and how do they relate to the derivative?
2. What is the significance of the second derivative in analyzing functions?
3. How would the approach change for higher-degree polynomials like in 884 or 885?
4. Would you like an explanation of how to classify critical points using $y''$?
5. How does finding the derivative help in understanding the behavior of functions?

Tip:

When solving for critical points, always check whether the derivative exists for all $x$ in the domain of the function!