What is -x^2+ 13x - 42 factored
1 answer:
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Answer:
a)
b)
The values are too small since is positive for both values of
in. I'm speaking of the
values, 2.9 and 3.1.
Step-by-step explanation:
a)
The point-slope of a line is:
where is the slope and
is a point on that line.
We want to find the equation of the tangent line of the curve at the point
on
.
So we know .
To find , we must calculate the derivative of
at
:
.
So the equation of the tangent line to curve at
is:
.
I'm going to solve this for .
Subtract 5 on both sides:
What this means is for values near
is that:
.
Let's evaluate this approximation function for .
Let's evaluate this approximation function for .
b) To determine if these are over approximations or under approximations I will require the second derivative.
If is positive, then it leads to underestimation (since the curve is concave up at that number).
If is negative, then it leads to overestimation (since the curve is concave down at that number).
is positive for
.
is negative for
.
That is, .
So is positive for both values of
which means that the values we found in part (a) are underestimations.
So firstly, we have to find f(x) when x = 8 and x = 0. Plug the two numbers into the x variable of the function to solve for their f(x):
Now that we have their y's, we can use the slope, aka average rate of change, formula, which is . Using what we have, we can solve it as such:
In short, the average rate of change from x = 0 to x = 8 is 5/21.