find the stationary point of f(x) = 2x^2 - 7x + 3

To find the stationary point of the function \( f(x) = 2x^2 - 7x + 3 \), we need to follow these steps:

1. **Find the derivative of the function**:  
   The derivative of \( f(x) \) with respect to \( x \) is \( f'(x) \).
   \[
   f'(x) = \frac{d}{dx}(2x^2 - 7x + 3) = 4x - 7
   \]

2. **Set the derivative equal to zero**:  
   A stationary point occurs where the derivative is zero.
   \[
   4x - 7 = 0
   \]

3. **Solve for \( x \)**:
   \[
   4x = 7
   \]
   \[
   x = \frac{7}{4} = 1.75
   \]

4. **Find the corresponding \( y \)-value**:  
   Substitute \( x = 1.75 \) back into the original function to find \( f(1.75) \).
   \[
   f(1.75) = 2(1.75)^2 - 7(1.75) + 3
   \]
   \[
   f(1.75) = 2(3.0625) - 12.25 + 3
   \]
   \[
   f(1.75) = 6.125 - 12.25 + 3 = -3.125
   \]

So, the stationary point is at \( (1.75, -3.125) \).

Would you like more details or have any questions?

Here are some related questions you might be interested in:
1. What is the nature (minimum or maximum) of the stationary point found?
2. How do you determine if a stationary point is a minimum, maximum, or point of inflection?
3. How would you find the stationary points of a cubic function?
4. What are the applications of finding stationary points in real-life scenarios?
5. How does the second derivative test help in classifying stationary points?

**Tip:** Stationary points are where the slope of the curve is zero, which can help in finding local maxima, minima, or points of inflection.

Learn how to find the stationary point of the function f(x) = 2x^2 - 7x + 3 with a detailed step-by-step solution. This problem covers calculus concepts, including derivatives and stationary points. Suitable for high school students.

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