Question

for what values of a and b does the function f(x)= x^3 + ax^2 + bx + 2 have a local maximum when x = -3 and a local minimum when x = -1?

Answer 1

find f '(x)

Answer 2

after that?

Answer 3

f(x)=x^3 + ax^2 + bx + 2
f'(x)=2x^2 +2ax+b

Isn't f'(x) = 3x^2 +2ax +b. 3 instead of 2 when differentiating.

Answer 4

oh man

Answer 5

tiaph has a point.

Answer 6

Think you need to find f''(x) also to differentiate the values of x that is the minimum and the maximum point, if not you will have 2 set of a and b values.

Answer 7

my monitor is far i can't focus

Answer 8

f(x)=x^3 + ax^2 + bx + 2
f'(x)=3x^2 +2ax+b
---------------------------
From the given points,
x=-3 x=-1
x+3=0 x+1=0
(x+3)(x+1)=0
x^2+4x+3=0 multiply whole equation by 3,
3x^2+12x+9=0
Compare

3x^2 +2ax+b
3x^2+12x+9

2a=12
b=9

Answer 9

there we go