![\bf f(x)=x+\cfrac{1}{x}\qquad \left[\frac{1}{2},2 \right]\\\\ -----------------------------\\\\ \cfrac{df}{dx}=1+\left(-1x^{-2} \right)\implies \cfrac{df}{dx}=1-\cfrac{1}{x^2} \\\\\\ f'(c)=1-\cfrac{1}{c^2}\quad \quad 1-\cfrac{1}{c^2}=\cfrac{f(2)-f\left( \frac{1}{2} \right)}{2-\frac{1}{2}} \\\\\\ 1-\cfrac{1}{c^2}=\cfrac{\frac{5}{2}-\frac{5}{2}}{\frac{3}{2}}\implies 1-\cfrac{1}{c^2}=\cfrac{0}{\frac{3}{2}}\implies 1-\cfrac{1}{c^2}=0 \\\\\\ 1=\cfrac{1}{c^2}\implies c^2=1\implies c=\pm\sqrt{1}\implies c=\pm 1](/tpl/images/0251/9847/a3c9b.png)
Checking the mean value theorem:
number 3
...
Answers: 1
Another question on Mathematics
Mathematics, 21.06.2019 18:20
Type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar. consider the given table.
Answers: 1
Mathematics, 21.06.2019 18:50
The random variable x represents the number of phone calls an author receives in a day, and it has a poisson distribution with a mean of 8.7 calls. what are the possible values of x
Answers: 1
Mathematics, 21.06.2019 19:20
Math each whole number with a rational,exponential expression
Answers: 1
Mathematics, 21.06.2019 23:40
What is the area of a rectangle with vertices (-8,-2), (-3,-2), (-3,-6), and (-8,-6)? units
Answers: 1
You know the right answer?
Questions
English, 12.01.2021 01:00
Mathematics, 12.01.2021 01:00
Mathematics, 12.01.2021 01:00
Mathematics, 12.01.2021 01:00
Advanced Placement (AP), 12.01.2021 01:00
History, 12.01.2021 01:00
English, 12.01.2021 01:00
French, 12.01.2021 01:00
Social Studies, 12.01.2021 01:00
History, 12.01.2021 01:00
