Differentiation question (1 Viewer)

[YBK]

Hey, we just started this topic at school and am sorta stuck on this question, which looks easy, and probably is

Differentiate y=x^2 + bx + c, and hence find b and c if:

a) The parabola passes through the origin and the tangent there has gradient 7


Well, I differentiated that and result was
dy/dx= 2x + b

Since it passes through origin that means a point that lies on the parabola is (0,0)

Therefore at (0,0) x=0 and y=0

replace that in the equation...? :s

There are quite a few questions that look like that in cambridge, and if I understand this, i'll get the rest... any help would be great!

Thanks!

 

[apak]

first you differentiate as you did
y=x^2+bx+c
y'=2x+b
if you know m of tan = 7
m of tan = y'
therefore 7=2x+b
you know at origin x=0 then b is 7
------------------------------------------------------------
* this bit is not apart of your question
from there you you have
y= mx+b y=7x+7 for the equation of the tan.
-------------------------------------------------------------

to find c you sub it bak
y=x^2 +7x+ c
0=0^2+0+c
c=0

 

[YBK]

first you differentiate as you did
y=x^2+bx+c
y'=2x+b
if you know m of tan = 7
m of tan = y'
therefore 7=2x+b
you know at origin x=0 then b is 7
------------------------------------------------------------
* this bit is not apart of your question
from there you you have
y= mx+b y=7x+7 for the equation of the tan.
-------------------------------------------------------------

to find c you sub it bak
y=x^2 +7x+ c
0=0^2+0+c
c=0

yay! thanks

had no idea that 2x+b = 7 !

 

[apak]

i just got one question. if your in yr 11, saying you do the hsc in 2006. how come you start diff now? arent you ment to have dont it mid year?

 

[YBK]

i just got one question. if your in yr 11, saying you do the hsc in 2006. how come you start diff now? arent you ment to have dont it mid year?

yeah, our teacher told us that she's going in-depth in the other topics. For example, we've done a lot on polynomials, co-ordinate geometry, circle geometry and algebra i think... ect

she said that this way it'd be an easier transition into the first 4unit maths topic.. complex numbers! She should be right..

 

[Riviet]

Yes, some decent knowledge on polynomials and trig will certainly help you out in the complex numbers topic, as alot of proofs are based on trig rules and the roots stuff with polynomials. However, you can still do it without the knowledge, complex numbers is the easiest topic in the 4u course.

 

[pLuvia]

i just got one question. if your in yr 11, saying you do the hsc in 2006. how come you start diff now? arent you ment to have dont it mid year?

You don't learnt geometric applications of calculus in year 11 I don't think?

 

[Slidey]

It depends on what school you go to, kadlil.

 

[pLuvia]

Well I learnt it in year 11 at tutor, but we weren't taught it at school

 

[HamuTarou]

is integraton in geometric applications of calculus?

sooner or later u'll learn it at skool kadlil, just wait ^_^

 

[Riviet]

is integraton in geometric applications of calculus?

sooner or later u'll learn it at skool kadlil, just wait ^_^

Geometric applications is also known as using differentiation to find stat. points and points of inflexion for a function and using these to help you sketch graphs. We're actually finishing it at my school at the moment. It's 2u work, so it should be straight forward for us 3/4 uniters. Integration is a separate topic.

 

[apak]

Geometric applications is also known as using differentiation to find stat. points and points of inflexion for a function and using these to help you sketch graphs. We're actually finishing it at my school at the moment. It's 2u work, so it should be straight forward for us 3/4 uniters. Integration is a separate topic.

well im a year 10 in my class we do stuff same as year 11 in our school. we did diff in the beginning of the year so.. integration is coming up next

 

[pLuvia]

hehe, I've already learnt integration in graphs and stuff, and learnt the volume etc etc

 

[Riviet]

hehe, I've already learnt integration in graphs and stuff, and learnt the volume etc etc

Haha same here

 

[acmilan]

The syllabus allows you to learn topics in any order, theoretically you are allowed to learn all the hsc topics in yr 11 and the prelim ones in yr 12

 

[DraconisV]

Well, im 3 unit we have done(so far in the hsc course) geometric applications of calculus and we have started series and sequences yesterday, so we will be done that topic by early next week.

 

[Riviet]

It looks like everyone is doing the topics in very different orders, and i guess there's nothing wrong with this.

 

[apak]

YBK
while your at it you might want to know:
f'(x) = y = dy/dx (all notations) = m (gradient) = 0 (at stationary points)
f''(x) = second derivative - shows the concavity of the curve when is positive it is concave down i think i was and concave up for the other one.. or the other way round = 0 at point of inflection (that is no concavity

 

[insert-username]

When f''(x) > 0, the curve is concave up.

When f''(x) < 0, the curve is concave down.

When f''(x) = 0, the curve is usually a point of inflexion, although this is not so with functions in the form axⁿ when n is positive and divisible by 2. In that case, the supposed point of inflexion is actually a minimum/maximum turning point depending on the sign of a.


I_F

 

[apak]

thankyou for adding in what i missed out. i was in school no time to complete... the bloody teacher was like " dont you understand english? You were told to turn off the comp" ... bloody ass