Solve x^3+2x^2-14x+2-3

$$x ^ { 3 } + 2 x ^ { 2 } - 14 x + 2 - 3$$

Differentiate w.r.t. x

$$3x^{2}+4x-14$$

Steps Using Derivative Rule for Sum

Subtract 3 from 2 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}+2x^{2}-14x-1)$$

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}.

$$3x^{3-1}+2\times 2x^{2-1}-14x^{1-1}$$

Subtract 1 from 3.

$$3x^{2}+2\times 2x^{2-1}-14x^{1-1}$$

Multiply 2 times 2.

$$3x^{2}+4x^{2-1}-14x^{1-1}$$

Subtract 1 from 2.

$$3x^{2}+4x^{1}-14x^{1-1}$$

Subtract 1 from 1.

$$3x^{2}+4x^{1}-14x^{0}$$

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

$$3x^{2}+4x-14x^{0}$$

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

$$3x^{2}+4x-14$$

Evaluate

$$x^{3}+2x^{2}-14x-1$$

Solution Steps

Subtract 3 from 2 to get -1.

$$x^{3}+2x^{2}-14x-1$$