Answer:
When we have a function f(x), the values of x at which the function is not differentiable are:
1) values at which the function is not "soft". So if we have a really abrupt change in the curvature of the function, we can not differentiate in that value of x, because in those abrupt changes there are a lot of tangent lines to them.
One example of this is the peak we can see at x = -4
Then we can not differentiate the function at x = -4
2) When we have a discontinuity.
If we have a discontinuity at x = x0, then we will have two possible tangents at x = x0, this means taht we can not differentiate at x = x0, and remember that a discontinuity at x = x0 means that:
f(x0₊) ≠ f(x0₋)
where x0₊ is a value that approaches x0 from above, and x0₋ is a value that approaches x0 from below.
With this in mind, we can see in the graph a discontinuity at x = 0, so we can not differentiate the function at x = 0.
Answer:
f(x) = x^2 -3
Step-by-step explanation:
A function is translated down 3 units by subtracting 3 from the function value. For the parent function f(x) = x^2, the translated function is ...
f(x) = x^2 -3
_____
<em>Comment on vertex form</em>
The full "vertex form" has the values of the vertex coordinates in the equation explicitly. For vertex (h, k), the form is ...
f(x) = a(x -h)^2 +k
We have moved the vertex from (0, 0) to (0, -3). The vertical scale factor (a) remains 1. So, we could write the equation as ...
f(x) = 1(x -0)^2 -3 . . . . vertex form with unnecessary parts shown
Removing the identity elements doesn't change anything (though it requires a little practice to see them when they aren't there). So, with minor simplification, this becomes ...
f(x) = x^2 -3
Answer:
I would say 70%
Step-by-step explanation:
He got 7 of of 10 (7/10 = 70%) right so I would say he would do just as well without ESP since it doesn't exist.
Answer:
Step-by-step explanation:
Let the first term be 
, then the terms of the sequence are:
.
Since the fourth term is 108, we have
Hence the sequence becomes:
.
The explicit expression for a geometric expression is given by:
where a=4 and r=3
The required formula is:
Answer:
351.9 cubic in
Step-by-step explanation:
The volume of a cylinder is hr²π.
r is half the diameter, so 8/2 is 4.
Plug in your h and r and get:
7 * 4² * π
7 * 16 * π
112π
Multiply the π and you'll get about 351.9 cubic in
