Answer:
a)


b)
The values are too small since  is positive for both values of
 is positive for both values of  in. I'm speaking of the
 in. I'm speaking of the  values, 2.9 and 3.1.
 values, 2.9 and 3.1.
Step-by-step explanation:
a)
The point-slope of a line is:

where  is the slope and
 is the slope and  is a point on that line.
 is a point on that line.
We want to find the equation of the tangent line of the curve  at the point
 at the point  on
 on  .
.
So we know  .
.
To find  , we must calculate the derivative of
, we must calculate the derivative of  at
 at  :
:
 .
.
So the equation of the tangent line to curve  at
 at  is:
 is:
 .
.
I'm going to solve this for  .
.


Subtract 5 on both sides:

What this means is for values  near
 near  is that:
 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).
 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 negative, then it leads to overestimation (since the curve is concave down at that number).



 is positive for
 is positive for  .
.
 is negative for
 is negative for  .
.
That is,  .
.
So  is positive for both values of
 is positive for both values of  which means that the values we found in part (a) are underestimations.
 which means that the values we found in part (a) are underestimations.