Quick Question? (1 Viewer)

[Zokunu]

littlehelp?

Differentiate from first principle y = x^2 +2

=2x

Find the gradient of the secant through the points A (1,3) and B (3,11) on this curve.

=4

Find the equation of the tangent to the curve at the point A

2x - y + 1 =0

Where does the tangent cut the x-axis

x = -1/2

Find the equation of the normal to the curve at the point B.????? <--------This?

 

[asianese]

What is the relationship between the gradient of the tangent and the gradient of the normal?

 

[Zokunu]

What is the relationship between the gradient of the tangent and the gradient of the normal?

Do i flip the gradient?

m=4 into m=-1/4?

soz if this is dumb...

 

[Menomaths]

That is correct

 

[asianese]

That's not dumb. THAT'S CORRECT!

 

[HSC2014]

Do i flip the gradient?

m=4 into m=-1/4?

soz if this is dumb...

Justify that step your solution. Why would you 'flip' it?

 

[Zokunu]

That's not dumb. THAT'S CORRECT!

w8 then what am i doing wrong here?

e) y-11= -1/4 (x-3)

y-11= -1/4x + 3/4

y= -1/4x + 47/4 ?

Answer: x + 6y = 69

 

[Makematics]

Justify that step your solution. Why would you 'flip' it?

He is right, you must understand why you are flipping it. (Hint: The normal, by definition, is perpendicular to the tangent)

 

[HeroicPandas]

w8 then what am i doing wrong here?

e) y-11= -1/4 (x-3)

y-11= -1/4x + 3/4

y= -1/4x + 47/4 ?

Answer: x + 6y = 69

u used m = -1/4 (which is the gradient of a line perpendicular to secant AB, which is not the gradient of the normal at B)

 

[Makematics]

w8 then what am i doing wrong here?

e) y-11= -1/4 (x-3)

y-11= -1/4x + 3/4

y= -1/4x + 47/4 ?

Answer: x + 6y = 69

The gradient of the tangent isn't 4

 

[Zokunu]

The gradient of the tangent isn't 4

Soz, but i'm a bit confused here..

 

[Zokunu]

Find the equation of the tangent to the curve at the point A
2x - y + 1 =0

I guess the gradient of the tangent here is 2?

Therefore the gradient of the normal is given by the perpendicular line properties? m1 x m2 = -1?

Is the gradient of the normal -1/2?

 

[bedpotato]

Yeah, but the question is asking for the equation of the normal at point B, not A. So find the gradient of the tangent at B (and so on).

 

[Zokunu]

Yeah, but the question is asking for the equation of the normal at point B, not A. So find the gradient of the tangent at B (and so on).

mhm, dw guys i got it now TY all. I got ONE MORE question related to this so pls help

(a) Differentiate from first principle y = x^3

3x^2

(b) Find the gradient of the secant though the points A and B on this curve, where x=1 and x=3 respectively. ?

Thanks

 

[Makematics]

mhm, dw guys i got it now TY all. I got ONE MORE question related to this so pls help

(a) Differentiate from first principle y = x^3

3x^2

(b) Find the gradient of the secant though the points A and B on this curve, where x=1 and x=3 respectively. ?

Thanks

You sub in x=1 and x=3 into y=x^3 to get the coordinates A(1,1) and B(3,27)
Then use the gradient formula to get gradient=13