- Difficulty
- Introductory
- Suggested time
- 3 min
- Marks
- 2
- Theory
- CLP-1 §2.13Key results
The Mean Value Theorem practice question 2
Find the value of in whose existence the Mean Value Theorem guarantees for on .
The theorem matches the slope of the tangent at with which other slope over ?
The theorem says . Compute the right-hand side, then solve that value.
A number, as a fraction or a decimal.
Theory CLP-1 §2.13Key results
Worked solution
Strategy
Compute the average rate of change over the interval, then find where the instantaneous rate equals it.
Working
Slope of the secant line.
Which lies in (1, 4), as the theorem promises.
Answer
The answer is five halves.
Check
For any quadratic the MVT point is the midpoint of the interval, and (1 + 4)/2 = 2.5.
Where this goes wrong
Setting f(c), not f′(c), equal to the secant slope 5, which gives √5. The theorem matches the slope of the tangent at c with the slope of the secant, so it is f′(c) that equals 5.
Leans on
Slope of a secant line, from The definition of the derivative
Try a similar question
Find the point promised by the Mean Value Theorem for on the interval .Saved in this browser only.