Slope of Tangent Line for f(x)=x^3+x at (2,10) | Algebraic Method

In summary, to find the slope of the tangent line of f at the given point (2, 10), you first take the derivative of f(x) using the power rule. Then, evaluate it at x = 2 to get the slope of the tangent line. This is the instantaneous rate of change at that point and is also known as f'(x).
  • #1
Mejiera
15
0

Homework Statement




find the slope of the tangent line of f at the given point.

Homework Equations



f(x)= x^3 + x at (2,10)

The Attempt at a Solution


I know how to get the answer using the power rule, but I want to know the algebraic way of doing it
I get stuck at x^3 + x - 10/ x -2 how do I get rid of the x-2 in the bottom ?
 
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  • #2
f'(x) is the instantaneous rate of change at any x on the graph of f(x). In other words, f'(x) is the exact slope at any point on the graph of f(x). First, take the derivative of f(x). Then from there you can evaluate for any x (in your case x=2) to find the slope of your tangent line.
 

1. What is the formula for finding the slope of a tangent line using the algebraic method?

The formula for finding the slope of a tangent line at a specific point (x0, y0) on a function f(x) is given by the derivative of the function, f'(x0).

2. How do you find the derivative of a function using the algebraic method?

To find the derivative of a function using the algebraic method, you must use the power rule. For a function f(x) = xn, the derivative is given by f'(x) = nx^(n-1).

3. What is the process for finding the slope of a tangent line using the algebraic method?

The process for finding the slope of a tangent line using the algebraic method involves finding the derivative of the function at the given point, substituting the x-coordinate of the point into the derivative, and simplifying the resulting expression to find the slope.

4. Can the slope of a tangent line be negative?

Yes, the slope of a tangent line can be negative. This occurs when the function is decreasing at the given point, meaning the tangent line has a negative slope.

5. How do you interpret the slope of a tangent line to a function at a specific point?

The slope of a tangent line to a function at a specific point represents the instantaneous rate of change at that point. It tells us how much the function is changing at that exact moment.

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