Consider the function f(x)=x^2-bx+c . Find f'(x)

Given the function \( f(x) = x^2 - bx + c \), let's differentiate it with respect to \( x \).

The derivative \( f'(x) \) of the function can be calculated using standard differentiation rules:

1. The derivative of \( x^2 \) is \( 2x \).
2. The derivative of \( -bx \) (where \( b \) is a constant) is \( -b \).
3. The derivative of a constant \( c \) is 0.

Thus, the derivative \( f'(x) \) is:

\[
f'(x) = 2x - b
\]

Would you like any further details or clarifications?

Here are 5 related questions:
1. How would the second derivative \( f''(x) \) look for the given function?
2. What is the significance of the derivative \( f'(x) \) in terms of the slope of the function?
3. How does the value of \( b \) affect the behavior of the derivative?
4. What would \( f'(x) \) be if \( b = 0 \)?
5. How can we find the critical points of the function using \( f'(x) \)?

**Tip**: When differentiating polynomials, apply the power rule: bring down the exponent and reduce it by one.

Consider the function f(x) = x^2 - bx + c. Find f'(x).

Explore how to differentiate the quadratic function f(x) = x^2 - bx + c. This solution uses the power rule of differentiation to find the derivative, f'(x) = 2x - b, and provides a detailed step-by-step explanation. Ideal for high school calculus students in Grades 10-12.

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