Thread: 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.

Hello, stewpot!

I don't understand the procedure you're using . . .
. . First Derivative Test for the "left side"?
. . Second Derivative Test for the "right side"?

Who told you to do it that way ??

Find and identify the stationary points for: .

Set the first derivative equal to zero: .

. . which factors:. .

. . and has roots: .

Stationary points: .


Second Derivative Test: .

. .

. .

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