Need help with AS Maths question :)

The question is:

The curve y=x^3+ax^2+bx+11 has a stationary point (3,-70).Find a and b and use this to determine whether (3,-70) is a local maximum or minimum.

I know I'm meant to use simultaneous equations this is what I got:

6a+b=-9 (by substituting the x and y values into the equation) and 3a+b=-36 (by making the derivative equal 0) which solve to get a=9 and b=-9

However the answer in the back says a=3 and b=-45. How do I get the right answer?

Reply 1

Math12345

14

Original post by lamp010101

The question is:

The curve y=x^3+ax^2+bx+11 has a stationary point (3,-70).Find a and b and use this to determine whether (3,-70) is a local maximum or minimum.

I know I'm meant to use simultaneous equations this is what I got:

6a+b=-9 (by substituting the x and y values into the equation) and 3a+b=-36 (by making the derivative equal 0) which solve to get a=9 and b=-9

However the answer in the back says a=3 and b=-45. How do I get the right answer?

y=x^3+ax^2+bx+11

Substitute in (3,-70): -70=27+9a+3b+11
9a+3b=-108
3a+b=-36 (you got this).

Next differentiate the equation: 3x^2+2ax+b
Substitute in (3,-70): 27+6a+b=0
6a+b=-27 (you did this wrong)

Then solve using simultaneous equations.

Reply 2

lamp010101

OP

3

Thank you so much! I differentiated wrong forgetting to decrease the power by one, I just got rid of it all together, Thank you for your help I really appreciate it!

Need help with AS Maths question :)

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