Solve f(x)=3x^3-9x^2+8x+1

$$f ( x ) = 3 x ^ { 3 } - 9 x ^ { 2 } + 8 x + 1$$

Differentiate w.r.t. x

$$\left(3x-4\right)\left(3x-2\right)$$

Steps Using Derivative Rule for Sum

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$3\times 3x^{3-1}+2\left(-9\right)x^{2-1}+8x^{1-1}$$

Multiply 3 times 3.

$$9x^{3-1}+2\left(-9\right)x^{2-1}+8x^{1-1}$$

Subtract 1 from 3.

$$9x^{2}+2\left(-9\right)x^{2-1}+8x^{1-1}$$

Multiply 2 times -9.

$$9x^{2}-18x^{2-1}+8x^{1-1}$$

Subtract 1 from 2.

$$9x^{2}-18x^{1}+8x^{1-1}$$

Subtract 1 from 1.

$$9x^{2}-18x^{1}+8x^{0}$$

For any term t, t^{1}=t.

$$9x^{2}-18x+8x^{0}$$

For any term t except 0, t^{0}=1.

$$9x^{2}-18x+8\times 1$$

For any term t, t\times 1=t and 1t=t.

$$9x^{2}-18x+8$$

Evaluate

$$3x^{3}-9x^{2}+8x+1$$