Can someone please check my homework?

Hi could one of the geniuses out there please check my homework?

Find the stationary points for f(x)=-2x^3+27x^2-84x+32

=-2(3x^2)+27(2x)-84(1)

=-6(x^2-9x+14)

=-6(x-2) (x-7)

Stationary points x=2 x=7

Then classify the left hand side using the First Derivative Test

x=2 xl=1 xr=3

f'(1)=-6(1) (-32) =190 >0

f'(3)= -6 (3) (-32) =-576 <0

So f has a local minimum at x=2

Classify the right hand side using the Second Derivative Test

x=7

Second derivative

-6(2x) + 54

=-12x + 54

=-6(2x - 9)

For stationary point x=7 xl=6 xr=8

f"(6) =-6((2x6)-(9x6))=252>0

f"(8) = -6((2x8)-(9x8)=336>0

Find the y coordinates x=2 x=7

f(2)= -16+1458-168+32=1306

f(7)=-56+5103-588+32 = 4491

I know theres a lot but would be greatful for any help.

Can you please show me how you arrived at this!

H Soroban,

Thanks for you speedy answer, I'm a little puzzled, can you break down how you arrived at the coordinates from [IMG]file:///Users/andystewart/Library/Caches/TemporaryItems/moz-screenshot.jpg[/IMG]-6(x-2)(x-7)=0.

I've tried most solutions and keep comming up with different coordinates!

Many thanks

Stewpot