As a check on our work in part (a), notice that if we let *a* = 3, then

*f* ′(*a*) = *f* ′(3) =

To evaluate \( f'(3) \), you'll need the derivative of the function \( f(x) \) from part (a). Since you haven't provided that function, I can guide you on how to proceed.

If you have the function \( f(x) \), follow these steps:

1. **Find the derivative**: Compute \( f'(x) \), the derivative of \( f(x) \).
2. **Substitute \( x = 3 \)**: Plug \( x = 3 \) into \( f'(x) \), i.e., calculate \( f'(3) \).

If you share the function \( f(x) \), I can compute the derivative and evaluate it for you.

Would you like further details or any clarification?

Here are five related questions to help further:
1. What is the original function \( f(x) \) from part (a)?
2. Do you need help finding the derivative of any function?
3. How does evaluating the derivative at a point help in analyzing the behavior of the function at that point?
4. Do you need assistance with differentiating specific types of functions (e.g., polynomials, trigonometric functions)?
5. Would you like to explore how the value of \( f'(a) \) relates to the slope of the tangent line at \( x = a \)?

**Tip:** Remember that \( f'(a) \) gives the instantaneous rate of change of the function \( f(x) \) at the point \( x = a \), which corresponds to the slope of the tangent line at that point.

As a check on our work in part (a), notice that if we let a = 3, then f′(a) = f′(3) =

Learn how to evaluate the derivative of a function at a specific point, f'(3). This problem focuses on differentiation and applying calculus concepts to find the slope of the tangent line. Suitable for students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation