1.) The interval of the value of x is from -5 to 1, inclusive. Remember that what is asked is the absolute value, thus the sign does not matter even if you have to subtract x from 5. Thus, the maximum value would be obtained if the x is smaller, which is 1. The minimum value is obtained when x=-5.
Absolute maximum value:
x = - 5f(-5) = ║5 - 7(-5)^2║ = ║-170║=
170Absolute minimum value:
x = 1f(1) = ║5 - 7(1)^2║ = ║-2║=
2
2.) The Mean Value Theorem (MVT) applies to functions that are continuous and differentiable on the closed and open interval of a to b, respectively. Since the function is a quadratic function, MVT can be applied. Then, this means that there is a value of c which is between a and b. This could be determined using this formula according to MVT:

The differentiated form would be f'(x) = -2x. Then,


Thus, x = -1, x = -1/2, and x=0 all lie in the function 4-x^2.
Answer:
3 1/3
Step-by-step explanation:
Right side segments are proportional to left side segments:
5/6 = x/4
x = 4·5/6 = 3 1/3 . . . . . multiply by 4
If there is such a scalar function <em>f</em>, then



Integrate both sides of the first equation with respect to <em>x</em> :

Differentiate both sides with respect to <em>y</em> :


Integrate both sides with respect to <em>y</em> :

Plug this into the equation above with <em>f</em> , then differentiate both sides with respect to <em>z</em> :



Integrate both sides with respect to <em>z</em> :

So we end up with

Answer:
A
Step-by-step explanation:
To know the distance between the two on a number line, we subtract both numbers from each other
Since the absolute value will give the same result irrespective of the number we used first, we can see that it is the first option that would give the needed results
This means that option A is our answer
Answer:
1. 50
2. 5
3.19
Step-by-step explanation: