C1 Solomon Paper B Question 2 Minimums

racshot65

Hi

How would you answer this ?

I've never seen a question like it

Reply 1

paronomase

one way of doing this, don't know if you learned it
you know that there is an extremum when the derivative is 0 for some point, and that the sign of the derivative changes at this point

Here, the derivative is y'=2x+a
then 2x+a=0 <=> x=-0,5a
Therefore, the minimum point of C is for x=-0,5a

You get -0,5a=-2 <=> a=4
For x=-2, y=5
Therefore, (-2)²+4*(-2)+b=5
so 4-8+b=5
and b=9

y=x²+4x+9

Reply 2

Marsha2112

It looks like simultaneous equations:
1st) Sub in yer values
5 = (-2)^2 -2a + b
5 = 4 -2a + b
1 = -2a + b

2nd) Differentiate to get y = 2x +a
You know as this is a minimum, it = 0
so 0 = 2(-2) + a
a = 4, sub that into your first one to find b :smile:

Reply 3

omjaikali

differentiate equation: = 2x + a
a minimum point is a stationary point, so dy/dx = 0
2x + a = 0
using (-2, 5) is a minimum point

and 2(-2) + a = 0
so a = 4
5= (-2)^2 +4(-2) +b
b = 9

Reply 4

adaggio123