Solve Shortest Distance Point (0,c) from Parabola y=x^2

Click For Summary
The discussion focuses on finding the shortest distance from the point (0,c) to the parabola y=x^2 for values of c between 0 and 5. The initial solution provided is (c-0.25)^0.5, but there is confusion regarding its validity for c values less than 1/4. Participants highlight that if c is less than 1/4, the solution does not apply, and suggest checking the endpoints of the interval to determine the nearest point on the parabola. The importance of considering the entire range of c values is emphasized to ensure a complete understanding of the problem. Clarifying these conditions is crucial for accurately solving the distance problem.
gaganpreetsingh
Messages
24
Reaction score
0
Hi I am stuck on this ques. although i have solved and got the ans but i am still facing a problem.
Find the shortest distance of the point (0,c) from the parabola y=x^2 where 0<= c <= 5
i got the ans right that is
(c-0.25)^0.5
but i have not been able to understand the use of the 0<= c <= 5
any help?
 
Physics news on Phys.org
any help out there?
 
Assuming that c> 1/4, I get that. However, notice that your solution makes no sense if c< 1/4! What is the nearest point on the parabola if c< 1/4? (Hint: check the endpoints of the interval of values for y.)
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Find the local maxima and minima for##f(x,y) = x^3-xy-x+xy^3-y^4##
  • · Replies 5 ·
Replies
5
Views
1K
Finding the Local Max/Min of f(x,y) on C
  • · Replies 14 ·
Replies
14
Views
2K
Find the constrained maxima and minima of ##f(x,y,z)=x+y^2+2z##
  • · Replies 2 ·
Replies
2
Views
2K
Parabola: Vertex =(?,0) and know 2 arbitrary points. How solve x?
  • · Replies 12 ·
Replies
12
Views
2K
Graphing Derivatives: How to Find Maxima, Minima, and Points of Inflection
  • · Replies 7 ·
Replies
7
Views
2K
Find all relative maxima/minima and saddle points
  • · Replies 2 ·
Replies
2
Views
2K
Maxima and minima of differential equation
  • · Replies 2 ·
Replies
2
Views
2K
What are the local maxima and minima of F(x)=(x^2)/(x+1)?
  • · Replies 3 ·
Replies
3
Views
2K
Maxima and minima of functions of two variables
  • · Replies 3 ·
Replies
3
Views
3K
Find the minimum value of area under y = 4x - x^3
  • · Replies 7 ·
Replies
7
Views
2K