# Applications of derivative.

• Jun 21st 2012, 01:27 PM
ftmtmr
Applications of derivative.
Determine the point on the curve y2=4x that is closest to the point (1,0).

AND

A fireman has to reach a burning building. Determine the length of the shortest ladder that will reach over a 2 metro high fence to the burning building which is 1 metro behind the fence.

• Jun 21st 2012, 02:35 PM
emakarov
Re: Applications of derivative.
Quote:

Originally Posted by ftmtmr
Determine the point on the curve y2=4x that is closest to the point (1,0).

Express the square of the distance between an arbitrary point (x, y) on the curve and (1, 0). It is easy to find the minimum of this expression.

Quote:

Originally Posted by ftmtmr
A fireman has to reach a burning building. Determine the length of the shortest ladder that will reach over a 2 metro high fence to the burning building which is 1 metro behind the fence.

The fireman would do well to use whatever ladder he has instead of doing calculus. (Smile) Let the base of the ladder be x meters from the building wall and let the top of the ladder touch the wall at y meters above the ground. Assuming the ladder touches the top of the fence, from the similarity of triangles we have y / x = 2 / (x - 1). Express y through x, find the square of the ladder length y2 + x2 in terms of x, then find the minimum of this expression using differentiation.
• Jun 22nd 2012, 03:17 AM
ftmtmr
Re: Applications of derivative.
Thanksss aloot :D i hope i will get good grade in the exam today.