Let f(x) = x³ – 2x² + x + 3

We need to find the derivative of f(x) i.e. f’(x)

We know that,

…(i)

f(x) = x³ – 2x² + x + 3

f(x + h) = (x + h)³ – 2(x + h)² + (x + h) + 3

Putting values in (i), we get

Using the identities:

(a + b)³ = a³ + b³ + 3ab² + 3a²b

(a + b)² = a² + b² + 2ab

Putting h = 0, we get

f’(x) = (0)² + 2x(0) + 3x² – 2(0) – 4x + 1

= 3x² – 4x + 1

Hence, f’(x) = 3x² – 4x + 1