someone pls help :)

[angel270]

can someone pls show me the working out and explanations for this question , thank u 

[Lilyyyy]

damn....I attempted but....what can I say...that's a tricky question

from my failed attempt I made a few observations...? (please correct me if I'm wrong)

the point P(-a,a) is actually a line of y=-x, so from that I tried to solve the distance between y=-x and f(x), my plan to construct a distance formula and then diff it make it into zero, but the 'b' term is giving me a lot of trouble. When you graph f(x), regardless of value of b, it's the same hyperbola looking shape so it's pretty clear the shortest distance would be from the most curved part (if you graph it this would make more sense) but I don't know how to get a general formula with the b term?

I'm sorry I didn't help at all ://

[fun_jirachi]

Hey there!

I honestly think it's more helpful that I give you pointers instead of the 'working out and explanations' for this question - it does seem like an assignment, so I do think it'll be handier in the long run that you do most of the work yourself.

So now, the pointers:
There are multiple ways to calculate minimum distances between a point and a curve. There are two ways I can think of off the top of my head:
a) constructing a distance function, proving that such a minimum exists, then finding the distance at that minimum, or
b) considering that for the distance to be a minimum, the line through the point (-a, a) that intersects the curve y=f(x) must be perpendicular to the tangent at the point of intersection - I'd be more inclined to explore this method, given that it does point you in the direction of part b) as well

Try exploring either of these, and preferably both - see why and how they work! It might also be helpful to use some graphing technology or your own graphing prowess to get a bit of a visual on the question.

If you're still stuck after this, I or someone else will gladly help you further! Hope this helps

[angel270]

damn....I attempted but....what can I say...that's a tricky question

from my failed attempt I made a few observations...? (please correct me if I'm wrong)

the point P(-a,a) is actually a line of y=-x, so from that I tried to solve the distance between y=-x and f(x), my plan to construct a distance formula and then diff it make it into zero, but the 'b' term is giving me a lot of trouble. When you graph f(x), regardless of value of b, it's the same hyperbola looking shape so it's pretty clear the shortest distance would be from the most curved part (if you graph it this would make more sense) but I don't know how to get a general formula with the b term?

I'm sorry I didn't help at all ://

thank u for attempting , i appreciate the effort xx

[angel270]

Hey there!

I honestly think it's more helpful that I give you pointers instead of the 'working out and explanations' for this question - it does seem like an assignment, so I do think it'll be handier in the long run that you do most of the work yourself.

So now, the pointers:
There are multiple ways to calculate minimum distances between a point and a curve. There are two ways I can think of off the top of my head:
a) constructing a distance function, proving that such a minimum exists, then finding the distance at that minimum, or
b) considering that for the distance to be a minimum, the line through the point (-a, a) that intersects the curve y=f(x) must be perpendicular to the tangent at the point of intersection - I'd be more inclined to explore this method, given that it does point you in the direction of part b) as well

Try exploring either of these, and preferably both - see why and how they work! It might also be helpful to use some graphing technology or your own graphing prowess to get a bit of a visual on the question.

If you're still stuck after this, I or someone else will gladly help you further! Hope this helps

thank u for the pointers !! i tried the question so many times earlier but couldn’t figure it out at all so i thought i’d post on the forum i’ll try again tho , thanks again x