Science:Math Exam Resources/Courses/MATH110/April 2014/Question 09 (c)
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q2 (a) • Q2 (b) • Q2 (c) • Q3 (a) • Q3 (b) • Q3 (c) • Q3 (d) • Q3 (e) • Q3 (f) • Q3 (g) • Q4 • Q5 • Q6 • Q7 (a) • Q7 (b) • Q8 (a) • Q8 (b) • Q9 (a) • Q9 (b) • Q9 (c) •
Question 09 (c) 

In some cases, the linear approximation of a function is equal to the function itself for all values of . What is one such function? 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Remember that the linear approximation is the tangent line at a particular point. 
Hint 2 

What might a function look like if it was equal to its tangent line at every point? 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Take the constant or linear function. We have . Then we just apply the linear approximation by finding and . Now we substitute.
We get the original function back. 