Solve =-lambda^3-3lambda^2-14

$$= - \lambda ^ { 3 } - 3 \lambda ^ { 2 } - 14$$

Differentiate w.r.t. λ

$$3\lambda \left(-\lambda -2\right)$$

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}.

$$3\left(-1\right)\lambda ^{3-1}+2\left(-3\right)\lambda ^{2-1}$$

Multiply 3 times -1.

$$-3\lambda ^{3-1}+2\left(-3\right)\lambda ^{2-1}$$

Subtract 1 from 3.

$$-3\lambda ^{2}+2\left(-3\right)\lambda ^{2-1}$$

Multiply 2 times -3.

$$-3\lambda ^{2}-6\lambda ^{2-1}$$

Subtract 1 from 2.

$$-3\lambda ^{2}-6\lambda ^{1}$$

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

$$-3\lambda ^{2}-6\lambda$$

Evaluate

$$-\lambda ^{3}-3\lambda ^{2}-14$$