What is the solution to the equation
2 answers:
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The absolute value function is defined as
If x is strictly positive (x > 0), then |x| = x, and d|x|/dx = dx/dx = 1.
If x is strictly negative (x < 0), then |x| = -x, and d|x|/dx = d(-x)/dx = -1.
But if x = 0, the derivative doesn't exist!
In order for the derivative of a function f(x) to exist at x = c, the limit
must exist. This limit does not exist for f(x) = |x| and c = 0 because the value of the limit depends on which way x approaches 0.
If x approaches 0 from below (so x < 0), we have
whereas if x approaches 0 from above (so x > 0), we have
But 1 ≠ -1, so the limit and hence derivative doesn't exist at x = 0.
Putting everything together, you can define the derivative of |x| as
Given:
The table of values.
To find:
The equation that best represents the relationship.
Solution:
From the given table it is clear that the value of x increasing by 2 and the value of y increasing by 3. Since y is increasing at a constant rate with respect to x, therefore the given table represents a linear relationship.
Consider any two points from the given table. Let the two points are (2,2) and (4,5). So, the equation of the line is
On further simplification, we get
Therefore, the correct option is A.