The natural logarithm in Mathematica...

Log[ 1 ]

0

Log[E]

1

Find extremes for a function

f[x_] := 3x^4 + 4x^3 - 12x^2 + 1

f[0]

1

D[f[x],x]

-24 x+12 (x^2)+12 (x^3)

f'[x]

-24 x+12 (x^2)+12 (x^3)

Solve[f'[x]==0,x]

{{x->-2},{x->0},{x->1}}

f[-2]

-31

f[1]

-4

Plot[ f[x], {x,-3,2}]