f[x_] := (Sin[4*x^2])^3 + 3*x

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

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

Show[p1, p2];

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

FindRoot[f'[x] == 0, {x, 0.65}]

FindRoot[f'[x] == 0, {x, 0.78}]

FindRoot[f'[x] == 0, {x, 0.90}]

FindRoot[f'[x] == 0, {x, 1.1}]

FindRoot[f'[x] == 0, {x, 1.3}]

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

FindRoot[f'[x] == 0, {x, 1.4}]

f[0.664751]

f[0.824935]

f[0.939484]

f[1.07166]

f[1.40921]

f[1.51047]

f[1.55872]

f[0]

f[Pi/2]

f[Pi/2] // N