Question:
Find the point (,) on the curve
that is closest to the point (3,0).
[To do this, first find the distance function between (,) and (3,0) and minimize it.]
Answer:

Step-by-step explanation:
can be represented as: 
Substitute
for 

So, next:
Calculate the distance between
and 
Distance is calculated as:

So:


Evaluate all exponents

Rewrite as:


Differentiate using chain rule:
Let


So:



Chain Rule:




Substitute: 

Next, is to minimize (by equating d' to 0)

Cross Multiply

Solve for x


Substitute
in 

Split

Rationalize



Hence:

19.00 3.50 11.00 4.47 makes it add up to hours so that will be answe C
Answer:
The distance is:
d = 10.0 units (Rounded to the nearest the Tenths Place)
Step-by-step explanation:
Given the points
The distance 'd' between (3,4) and (4,-6)


substituting the points values




units (Rounded to the nearest the Tenths Place)
Thus, the distance is:
d = 10.0 units (Rounded to the nearest the Tenths Place)
Use a number line if you need 4/10 - 6/10 = -2/10a simpler way is to do the opposite 6/10 - 4/10 = 2/10 then the answer would be the opposite as well. so, -2/10