Year 12s: what will be the first way you research your future options? >>

C1 Soloman Integration help pls :3

12) The curve C with the equation y=f(x) is such that

dy/dx= k - x^-1/2 , where k is a constant.

Given that C passes through the points (1,-2) and (4,5)

a) Find the value of k.

I used simultaneous equations and got some weird fraction. Don't think it's right because it links to part b

b) Show that the normal to C at the point (1,-2) has the equation x + 2y + 3 = 0

Thank you :blushing:

Reply 1

Dinaa

Also a graphs function question if you're feeling generous :mmm:

3a) Show that the line y=4x + 1 does not intersect with the curve y=x^2 + 5x + 2.

Done that :smug:

b) Fine the value of m such that the line y=mx + 1 meets the curve y= x^2 +5x +2 at exactly one point.

:K:

Reply 2

brianeverit

Original post by Dinaa

Unparseable latex formula:

y=kx-2\sqrtx+C

substititute the coordinates of the two points and solve simultaneously giving

k=3

Reply 3

Dinaa

Original post by brianeverit

Unparseable latex formula:

y=kx-2\sqrtx+C

substititute the coordinates of the two points and solve simultaneously giving

k=3

Oh oops, I integrated wrong :blushing:

Thank you

Reply 4

brianeverit

Original post by Dinaa

Also a graphs function question if you're feeling generous :mmm:

3a) Show that the line y=4x + 1 does not intersect with the curve y=x^2 + 5x + 2.

Done that :smug:

b) Fine the value of m such that the line y=mx + 1 meets the curve y= x^2 +5x +2 at exactly one point.

:K:

y=mx+1

only meets the curve

y=x^2+5x+2

at one point then it must be a tangent to the curve hence the simultaneous solution must produce equal roots. Do you know the condition for this to happen ?

(edited 8 years ago)

Reply 5

Dinaa

Original post by brianeverit

If [text]y=mx+1\text{ only merts the cutve y=x^2+5x+2 \text{ at one point then it must be a tangent to the curve }

hence the simultaneous solution must produce equal roots.
Do you know the condition for this to happen ?

Message is kind of funky :colondollar:

Reply 6

Dinaa

Original post by brianeverit

y=mx+1

only meets the curve

y=x^2+5x+2

at one point then it must be a tangent to the curve hence the simultaneous solution must produce equal roots. Do you know the condition for this to happen ?