Differentiation (with co-ordinates) :):):) (1 Viewer)

[Smile12345]

Hello All...

Could someone please help me with these Q's?

1. If the tangent at P(a,b) on the curve y= 6 / x cuts the y-axis at T(0,3), find the co-ordinates of P.

2. If y = 6x - 11 touches the parabola y = ax^2 + bx + 1 at the point (2,1), find the values of a and b...


Thanks for your help in advance.

 

[cookiez69]

1)
dy/dx = -6/x^2 (Gradient of the tangent at any particular x-value)
Finding the equation of the tangent:
y-3=(-6/x^2)(x-0)

Since we need to find the point of intersection, sub in y=6/x
6/x - 3 = -6/x
12/x = 3
12=3x
x=4 (This is your 'a')

sub into y=6/x
y=6/4 = 3/2
Therefore P(3, 3/2)

2)
dy/dx = 2ax + b
2ax + b = 6
2a(2) + b =6
4a + b = 6 ... (1)

y=ax^2 + bx + 1
1 = a(2)^2 + b(2) + 1
4a + 2b = 0 ... (2)

(2)-(1)
b=-6
Sub into (2)
4a+2(-6)=0
4a=12
a=3

Therefore a = 3 , b = -6

 

[Smile12345]

Thanks heaps...