Solve x^3-4x^2+7x-13

$$x ^ { 3 } - 4 x ^ { 2 } + 7 x - 13$$

Differentiate w.r.t. x

$$3x^{2}-8x+7$$

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}.

$$3x^{3-1}+2\left(-4\right)x^{2-1}+7x^{1-1}$$

Subtract 1 from 3.

$$3x^{2}+2\left(-4\right)x^{2-1}+7x^{1-1}$$

Multiply 2 times -4.

$$3x^{2}-8x^{2-1}+7x^{1-1}$$

Subtract 1 from 2.

$$3x^{2}-8x^{1}+7x^{1-1}$$

Subtract 1 from 1.

$$3x^{2}-8x^{1}+7x^{0}$$

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

$$3x^{2}-8x+7x^{0}$$

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

$$3x^{2}-8x+7\times 1$$

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

$$3x^{2}-8x+7$$

Evaluate

$$x^{3}-4x^{2}+7x-13$$