f[x_] = x^5 + 2  x^4 - x^3 - 2  x^2

f'[x]

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

N[%]

Plot[f[x], {x, -5, 5}]

FindRoot[f'[x] == 0, {x, -1.5}]

FindRoot[f'[x] == 0, {x,  .7}]

FindRoot[f'[x] == 0, {x, 0}]

FindRoot[f'[x] == 0, {x, - .7}]

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

\(□\&\(Increasin\ from\ \((\(-∞\), \(-1.67279\))\); \((\(- .656116\), 
            0)\); \(( .728902, ∞)\)

          
          Decreasing\ from\ \((\(-1.67279\), \(- .656116\))\); \((0,  .728902)\)\)\)

g[x_] = (5  x^2 - 4  x - 7)/(3  x^2 - x - 14)

Plot[g[x], {x, -10, 10}]

g''[x]

Plot[g''[x], {x, -10, 10}]
s = Factor[-14 - x + 3  x^2]

Solve[2 + x == 0]

Solve[-7 + 3  x == 0]

Limit[g[x], x -> Infinity]

Limit[g[x], x -> -Infinity]

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

N[%]

FindRoot[g''[x] == 0, {x, 20}]

FindRoot[g''[x] == 0, {x,  .1}]