Maximum volume from a rectangular cardboard

[Karol]

Homework Statement

Homework Equations

First derivative=maxima/minima/vertical tangent/rising/falling
When f'(x)>0 → the function rises

The Attempt at a Solution

$$V=(15-2a)(8-2a)=4a^2-46a+120$$
$$V'=8a-46,~~V'=0\rightarrow a=5.75$$
But: $~2a<8,~~V(a=4)=0$
So 5.75>4
And: $~V''=8$ so it holds water, it should be inverse.

 

[Nidum]

V=(15−2a)(8−2a) = 4a2−46a+120V = (15−2a)(8−2a)=4a2−46a+120​

V=(15−2a)(8−2a) ? or Volume = length x breadth ? That can't be right can it ?

How many dimensions do you need to multiply together to get the volume of a box ?

 

[Karol]

$$V=(15-2a)(8-2a)a=4a^3-46a^2+120a$$
$$V'=12a^2-92a+120,~V'=0\rightarrow a=1\frac{2}{3}$$
Thank you Nidum