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first you need to find the slope at this point

-2x ?

that is the function of all the slopes wrt to x

the point where it touches f(x) which is below the x axis?

take a look at your point

(5, 0)

whats the x value of the point

right so we need to know f'(5) = ?

But that point doesn't even lie on the curve...

we just want the slope there at x=5

so that would be -2(5) = -10, right?

oh wait 5,0 isnt on this curve really?

u are right lol xD

Yeah cause try plugging it in the function

XD

I think we should first find a point that apparently lies somewhere under the x-axis

k lets graph and see what exactly is going on here

|dw:1435217659239:dw|

|dw:1435217751709:dw|

okay so eventually this has to happen, they want us to find this x,y

Yep!

So are we solving for the secant line?

between (5,0) and (a, 9-a^2)

you already got that the slope was
F'(x)=-2x

right

Right

now write the slope with those 2 points

and equate it to the F'(x)

|dw:1435217973229:dw|

Yeah lol i was typing the same xD

We get a quadratic equation when we solve for a... that means we'll get 2 values for a...

a^2 - 10a + 9 = 0

thats a 9 :P

yes

Yes, two tangent lines can be drawn to a parabola form an external point

lol xD ok so a=1 and x=9 ? Is that right?

i mean a* = 9

|dw:1435218241639:dw|

a=9 is right, but how did u figure ?

but neither of the 2 points i found for 'a' lie under the x-axis

I solved the quadratic a^2 -10a +9

okay i see you simply discarded a=1 without any reason

nope i wrote that as well lol ^^ check again :P

What happens next?

Okay just making sure :)
plugin x=a=9 into the equation, you do get a point under the x axis

I do? Ohh thats right! xD

So that means I get 2 tangent lines?

Ohh nice!!

I love discarding stuff in math xD haha

lol we're very much alike :P

i am not following exactly what u are doing here ganeshie
y=m(x-5)
y=9-x^2

are u then setting m=-2x to solve it

solving that gives the slope of two tangent lines passing thru (5, 0)

oh i see! what you mean i didnt understand what discriminant meant lol

nice trick

neither did I o.o XD lol

Lol that had me confused to but I was too scared to ask, nice one.

thats okay, stick to dan's method as it is more calculussy

I feel like an idiot now xD

@Astrophysics pshhhh in that case i'm more of an idiot that everyone! XD lol

reminds me of 3 idiots movie

Ahhh i see

|dw:1435219094311:dw|

Lmao XD truuueee :D so much humour the night before my exam :D lol

hmmm i see it now

|dw:1435219226919:dw|

Yep! Got it all :)

k good

Thanks so much!!! :)

yeah sure =]

Thank you teachers!

Yeshh :D

Are all these questions part of a practice exam?

Yeah, they're some sample/practice questions... or whatever they call it XD lol

@Astrophysics :D sorry about the late response, wasn't paying attention lol

Lol no worries was helping someone anyways, haha and good luck, calc exams have always been long >.<

thank you! :) Yeah it's gonna be 2.5 hours 8:30 in the morning >.<

Eek, haha get some sleep as well! Later :P

I'd better xD lol otherwise its a big fat 0 xD haha