1. Find an equation of the tangent line to the curve at the point (2,3)
The Tangent Problem
Find an equation of the tangent line to the curve at the point (2,3)

2. First we need to estimate the slope at the point (2,3).

3. We are going to estimate the slope using secant lines

4. From the left: Using points (2,3) and (1,-1)

5. From the left: Using points (2,3) and (1.5, -0.375)

6. From the left: Using points (2,3) and (1.9, 2.069)

7. From the left: Using (2,3) and (1.99,2.9007)

8. From the right: Using points (2,3) and (3,21)

9. From the right: Using points (2,3) and (2.5,9.875)

10. From the right: Using points (2,3) and (2.1, 4.071)

11. From the right: Using (2,3) and (2.01, 3.1007)

12. Summary of Results
Point (x,y)
Slope of secant line between (2,3) and point (x,y)
(1, -1) 4
(3, 21) 18
(1.5, )
6.75
(2.5, 9.875)
13.75
(1.9, 2.069)
9.31
(2.1, 4.071)
10.71
(1.99, )
9.9301
(2.01, )
(1.999, )
9.993
(2.001, )
10.007
From both the left and the right sides, the slopes of the secant lines are approaching 10, so we can estimate that the slope of the tangent line to the point (2,3) is 10.

13. Original Question: Find an equation of the tangent line to the curve at the point (2,3)
We know that m = 10 and we have a point (2,3), so