Need help for differentiation (1 Viewer)

[fullonoob]

ok i got this question for tutor and i don't know how to do it

Find the equations of the tangents to the curve y=x^2-2x-3 at the points where the line y=5 cuts the parabola. Find also the point of intersection of these tangents.

Help plz>>>show all working out
Thx

 

[jellybelly59]

ok i got this question for tutor and i don't know how to do it

Find the equations of the tangents to the curve y=x^2-2x-3 at the points where the line y=5 cuts the parabola. Find also the point of intersection of these tangents.

Help plz>>>show all working out
Thx

y = x^2 - 2x - 3
5 = x^2- 2x - 3
0 = x^2 - 2x - 8
0 = (x - 4 )(x + 2)

intersection pts = (4,5) and (-2,5)

y' = 2x-2
y'(4) = 2(4) - 2
y' (4) = 6
(6/1) = (y-5)/(x-4)
6x-19=y ------> tangent of (4,5)

y' = 2x-2
y'(-2) = 2(-2) -2
y = -6
(-6/1) = (y-5)/(x+2)
-6x-7 = y ----> tangent of (-2,5)

6x-19 = -6x-7
12x= 12
x=1
6(1)-19 =-6(1)-7
-13 = -13

 

[Aquawhite]

ok i got this question for tutor and i don't know how to do it

Find the equations of the tangents to the curve y=x^2-2x-3 at the points where the line y=5 cuts the parabola. Find also the point of intersection of these tangents.

Help plz>>>show all working out
Thx

That's pretty advanced maths for year 10. I'm in the top class and we havn't started that yet (the teacher said we would do a little bit). I understood most of where your coming from though because I was trying to combine my knowledge of algebra... trig and geometry in graphs all together lol.

Seems pretty hard.

 

[Doctor Jolly]

That's pretty advanced maths for year 10. I'm in the top class and we havn't started that yet (the teacher said we would do a little bit). I understood most of where your coming from though because I was trying to combine my knowledge of algebra... trig and geometry in graphs all together lol.

Seems pretty hard.

I don't think differentiation should be in the Year 10 Syllabus and I don't think teachers should be teaching Calculus yet. But once you get to do it, it's pretty fun actually

 

[Aquawhite]

I don't think differentiation should be in the Year 10 Syllabus and I don't think teachers should be teaching Calculus yet. But once you get to do it, it's pretty fun actually

It looks like its pretty fun to do! (in class with my teacher because she's just AWESOME). In my ext1 maths next year my teacher said we would get straight into calculus in the differentiation topic. well the basics first . lol.

 

[lyounamu]

I am guessing that OP might be accelerated.

 

[Continuum]

jellybelly, the OP goes to the same school as you.

I've never heard of them being able to accelerate at maths though.

 

[rolror88]

ok i got this question for tutor and i don't know how to do it

Find the equations of the tangents to the curve y=x^2-2x-3 at the points where the line y=5 cuts the parabola. Find also the point of intersection of these tangents.

Help plz>>>show all working out
Thx

Who says tutors can't accelerate their own students?

 

[-tal-]

y = x^2 - 2x - 3 y = 5 cuts the parabola

Sub y = 5 into y = x^2 - 2x - 3
x^2 - 2x - 3 = 5
x^2 - 2x - 8 = 0
(x + 2)(x - 4) = 0
x = -2 or x = 4
therefore, the 2 points are (-2,5) and (4,5) [since y=5 cuts the parabola]


y' = 2x - 2 let y' = f(x)
f(-2) = -4 - 2
= -6 = gradient (m) of tangent @ (-2,5)
Eqn of tangent @ (-2,5):
y - 5 = -6(x - -2)
y = -6x - 7 ... 1


f(4) = 2(4) - 2 = 6 = gradient (m) of tangent @ (4,5)
Eqn of tangent @ (4,5):
y - 5 = 6(x - 4)
y = 6x - 19 ... 2


1 = 2
- 6x - 7 = 6x - 19
12x = 12
x = 1

Sub x = 1 into both eqns
y = -6(1) - 7 = 6(1) - 19
y = -13

point of intersection is (1,-13)

 

[Continuum]

Who says tutors can't accelerate their own students?

I didn't read that part. Shoot me.

 

[rolror88]

I have no gun . lol. I envy those schools which offer accelerated subjects.

 

[fullonoob]

wat's an OP xP
I'm doing accelerated for tutor...differentiation is not in yr10 syllabus

 

[Aplus]

I am guessing that OP might be accelerated.

It might be an advanced tutor lol.

 

[AnandDNA]

im in yr 11 and still havent done differentiation

 

[rolror88]

wat's an OP xP
I'm doing accelerated for tutor...differentiation is not in yr10 syllabus

Original Poster

 

[Doctor Jolly]

im in yr 11 and still havent done differentiation

It's not even in my school's syllabus for year 11. Lucky I've already learnt it at tutoring

 

[kaz1]

I don't think we do it in year 11 either. But I learnt it myself.

 

[Continuum]

Uhh... I'm pretty sure it is in the Year 11 syllabus.

 

[forkyspoony18]

Uhh... I'm pretty sure it is in the Year 11 syllabus.

I didn't start differentiation until the very first term of year 12 at my school...

 

[Continuum]

Really? It says you should've done it in the syllabus:

Tangent to a curve and derivative of a
function (8.1–8.9)