From your input, it seems you're trying to optimize the function y = x^2 + 3x - 10 and find its minimum value. Your background in basic calculus will definitely be beneficial, and I'll help fill in the blanks with regards to gradient descent. Let's dive right in. The gradient descent algorithm is an iterative optimization algorithm used to find the minimum of a function. Here's how it works in simple steps: 1. Initialization: We start with a random point in our function. 2. Calculate Gradient: We then calculate the gradient at that point, which gives us the direction of the steepest ascent. Since we want to go downwards (we're trying to find the minimum), we'll go in the opposite direction. 3. Update Point: We then take a step in the direction of the steepest descent and land on a new point. 4. Iterate: We repeat steps 2 and 3 until we can no longer move downwards. Applying gradient descent to your function: 1. The derivative of your function, which represents the gradient, is 2x + 3. 2. Let's choose a random starting point, say x = 0. 3. Now we iteratively update x using the rule: x = x - alpha * (2x + 3), where alpha is the learning rate. A common starting point for alpha is 0.01. 4. We repeat the update until x doesn't change significantly. Here's an ASCII representation of the function and the iterative process: 20 - 19 - * 18 - * 17 - * 16 - * 15 - * 14 - * 13 - * 12 - * 11 -* 10 - 9 - 8 - 7 - 6 - 5 -* 4 - 3 - 2 - 1 - 0 --------------------------------- In the chart above, each '*' represents the value of x in each iteration as it moves down the slope of the function. By running the process for enough iterations, you should get a minimum value for the function. Remember, this is a simplification and actual implementation would involve some more fine-tuning, like adjusting the learning rate alpha as needed. If you have more questions or need further clarification, feel free to ask!