Answer:
(a)
The function f is continuous at [1,e] and differentiable at (1,e), therefore
the mean value theorem applies to the function.
(b)
= 1.71828
Step-by-step explanation:
(a)
The function f is continuous at [1,e] and differentiable at (1,e), therefore
the mean value theorem applies to the function.
(b)
You are looking for a point 
such that
You have to solve for and get that
= 1.71828
Answer:
41. f⁻¹(x) = -9x + 4
43. m⁻¹(x) = ∛(x-2)/4
Step-by-step explanation:
41. y = (4-x)/9
swap x and y: x = (4-y)/9
solve y: 9x = 4-y
y = -9x + 4
45. y = 4x³+2
x = 4y³+2
4y³ = x-2
y³ = (x-2)/4
y = ∛(x-2)/4
Let you do 42 and 46 by yourself
Answer:
24
Step-by-step explanation:
In order to find the volume of something you would have to multiply the width x the length x the height which is 3x2x4 which equals to 24.
Solve for y...
2xy=1
y=1/(2x)
So this is a function as each x value (with the exception of x=0) produces just one value for y. However, technically there is a vertical asymptote about the vertical line x=0. So there is a discontinuity as x=0.
I say this technically, because most would say that this function is true even with the discontinuity (as they do with say y=tana), but technically the discontinuity makes this not a function because another requirement of a function is for their to be an actual output value for each input value. In this case division by zero when x=0 is undefined and cannot be included as part of a function. So if you are picky about being absolute, 2xy=1 is really two functions. One with a domain of (-oo,0) and another with a domain of (0,+oo).
