Asked by mike
                there are two tangents lines to the curve f(x) = 3x^2 that pass through the point p =0,1 find the x coordinates of the point where the tangents line intersect the curve
            
            
        Answers
                    Answered by
            Reiny
            
    The point (0,1) lies in the "interior" of the parabola
y = 3x^2.
There is no tangent to the curve that will pass through (0,1).
check your typing.
    
y = 3x^2.
There is no tangent to the curve that will pass through (0,1).
check your typing.
                    Answered by
            mike
            
    there are two tangents lines to the curve f(x) = 3x^2 that pass through the point p =0,-1 find the x coordinates of the point where the tangents line intersect the curve, please show working.
    
                    Answered by
            Reiny
            
    ahhh, now it makes sense.
let the point of contact be (a,b)
slope of tangent by the grade 9 way = (b+1)/a
slope of tangent by Calculus is
dy/dx = 6x
so at the point (a,b), slope = 6a
then 6a = (b+1)/a
6a^2 = b+1
but since (a,b) lies on the curve, b = 3a^2
so
6a^2 = 3a^2 + 1
a^2 = 1/3
a = ± 1/√3
so the x coordinates of the two tangents are 1/√3 and -1/√3
    
let the point of contact be (a,b)
slope of tangent by the grade 9 way = (b+1)/a
slope of tangent by Calculus is
dy/dx = 6x
so at the point (a,b), slope = 6a
then 6a = (b+1)/a
6a^2 = b+1
but since (a,b) lies on the curve, b = 3a^2
so
6a^2 = 3a^2 + 1
a^2 = 1/3
a = ± 1/√3
so the x coordinates of the two tangents are 1/√3 and -1/√3
                    Answered by
            mike
            
    find the equation of the tangent line of the curve y=root x divideed by x+1 at the point p = 2, root 2 divided by 3. show working please.
    
                    Answered by
            mike
            
    find the equation of the tangent line to the curve y = 2√2/x+1 at the point p=1,2/3.please show working. i would appreciate if you do it before 12:05pm today
    
                    Answered by
            mike
            
    use implcit differenciation to find an eqaution of both the tangent line to the ellipse:
2x^2 + 4y^2 = 36
that passes through the points: 14,3
 
    
2x^2 + 4y^2 = 36
that passes through the points: 14,3
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