- Topic
- Linear approximation
- Difficulty
- Introductory
- Suggested time
- 2 min
- Marks
- 1
Linear approximation practice question 2
The linear approximation of a function about is . What are and ?
The linear approximation is the tangent line at 2: it passes through and has slope .
The slope of is its coefficient of . For , evaluate at the base point , not at .
Theory UBC Math 100 §9.2CLP-1 §3.4Key results
Worked solution
Strategy
The tangent line shares the function’s value and slope at the base point, and nothing else. Read both off the line.
Working
Coefficient of x.
The line agrees with f at the base point.
Answer
The answer is f of 2 is 1 and f prime of 2 is 4.
Check
The line through (2, 1) with slope 4 is y = 1 + 4(x − 2) = 4x − 7, the L given.
Where this goes wrong
Reading f(2) as the intercept −7. The intercept is L(0), the value at x = 0, which tells you nothing about f; only the value at the base point 2 is shared.
Leans on
Slope-intercept form of a line, from Functions, graphs and inverses
Try a similar question
Use a linear approximation of at to estimate .Saved in this browser only.