The discussion centers on finding the second derivative of the volume of a cube with respect to the length of a side. The correct formula for the volume of a cube is V(x) = x³, where x is the length of a side. The initial suggestion of f(x) = x³/x = x² is incorrect, as it represents the surface area of a single face rather than the volume. To find the second derivative, one must first differentiate V(x) = x³ to obtain V'(x) = 3x², and then differentiate again to find V''(x) = 6x.
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Why do you have f(x) = x3/x = x2? Wouldn't that just be the surface area of a single face of the cube rather than it's volume?dunit909 said:I am asked to find the second derivative of the volume of a cube with respect to the length of a side.
would my initial f(x)=x3/x ??
than just follow with the quotient rule to get f(2)(x)?