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 ).
Answer:
7 + (9n) >= -29 (more or equal)
Step-by-step explanation:
0.01. All you have to do is reverse it so divide .1 by 10
The answer is an equation, a condition:
f(x) = f^(-1)(x), then apply f(x) again: f(f(x) ) = f(f^-1(x)) = x,
f(f(x)) =x, that means that:
The point of intersection is the point where applying f(x) twice it results in the identity. A similar argument takes you to f^(-1)(f^(-1)(x)) = x.
Furthermore, the final answer is the point where f(x)=x (which coincides with f^(-1)(x)=x). That is the value of x where the function crosses the line y=x. If there is no such point, then f(x) and f^(-1)(x) will never cross each other.
I can see the proof graphically, so I can't post it.
For a line, it always works:
f(x) = ax+b, f^(-1)(x) = (x-b)/a, ax+b = (x-b)/a --> a^2x+ab=x-b,
x = -(a+1)*b/(a^2-1) = -b/(a-1). Which is indeed where f(x)=x.
Answer:
x^3 + 9x^3 -6x -54
Step-by-step explanation:
first step is you're going to simplify the problem.
using the (a-b)(a+b)=a^2-b^2 formula combine the last two grouped numbers to equal (x+9)(x^2-6)
multiply the parenthesis to get x^3 - 6x + 9x^2 -54
reorder the terms and then you get your answer! x^3 + 9x^3 -6x -54
does this make sense? :)
