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The Mean Value Theorem:
If a function is continuous on [ a, b ] and differentiable on ( a , b ) than there is a point c in ( a, b ) such that:
f ` ( c )= ( f ( b ) - f ( a ) ) / ( b - a )
f ` ( c ) = ( f ( 2 ) - f ( 0 ) ) / ( 2 - 0 )
f `( x ) = 10 x - 3
f ` ( c ) = 10 c - 3
2 f ` ( c ) = 16 - 2
f ` ( c ) = 7
7 = 10 c - 3
c = 1
Answer:
Yes, the function is continuous on [ 0, 2 ] and differentiable on ( 0, 2 ).
For this case we must solve the following equation:
![\frac {x + 4} {3} = 2](https://tex.z-dn.net/?f=%5Cfrac%20%7Bx%20%2B%204%7D%20%7B3%7D%20%3D%202)
We follow the steps below:
Multiplying by 3 on both sides of the equation we have:
![x + 4 = 3 * 2\\x + 4 = 6](https://tex.z-dn.net/?f=x%20%2B%204%20%3D%203%20%2A%202%5C%5Cx%20%2B%204%20%3D%206)
Subtracting 4 from both sides of the equation:
![x = 6-4\\x = 2](https://tex.z-dn.net/?f=x%20%3D%206-4%5C%5Cx%20%3D%202)
Thus, the solution of the equation is![x = 2](https://tex.z-dn.net/?f=x%20%3D%202)
Answer:
![x = 2](https://tex.z-dn.net/?f=x%20%3D%202)
Answer:
1/3 is the answer
Step-by-step explanation:
Answer:
D between x=4 & x=6
Step-by-step explanation:
0-3 3 numbers 0-2
3-11 8 numbers 2-4
11-23 12 numbers 4-6