Question

Plesae help me.......
I have the answer can somone please check me....
Find values for a and b so that f(x)=x^3+ax+b
has a relative minimum at (2,-9)
a=? b=?

Answer 1

a=-12 b=4

Answer 2

so the point (2, -9) needs to be on the curve

so if you substitute into the equation you get


-9 = (2)^3 + 2a + b


or

-17 = 2a + b

you also knoq that (2, -9) is a minimum... so the value of the gradient at the point is zero.

so the 1st derivative is

f'(x) = 3x^2 + a

and if f'(x) = 0 when x = 2

then

0 = 3(2)^2 + a

or

- 12 = a

substitute it into the original equation to find b.