f[x_] := (-2*x^3 + 5*Sqrt[x] + 4)^2

p1 := Plot[f[x], {x, 0, 2}]

p2 := Plot[f'[x], {x, 0, 2}]

Show[p1, p2];

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

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

f[0]

f[0.704556]

f[1.74364]

f[2]

f[2] // N