Solve -lambda^3+4lambda^2+lambda+2

$$- \lambda ^ { 3 } + 4 \lambda ^ { 2 } + \lambda + 2$$

Differentiate w.r.t. λ

$$1+8\lambda -3\lambda ^{2}$$

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}.

$$3\left(-1\right)\lambda ^{3-1}+2\times 4\lambda ^{2-1}+\lambda ^{1-1}$$

Multiply 3 times -1.

$$-3\lambda ^{3-1}+2\times 4\lambda ^{2-1}+\lambda ^{1-1}$$

Subtract 1 from 3.

$$-3\lambda ^{2}+2\times 4\lambda ^{2-1}+\lambda ^{1-1}$$

Multiply 2 times 4.

$$-3\lambda ^{2}+8\lambda ^{2-1}+\lambda ^{1-1}$$

Subtract 1 from 2.

$$-3\lambda ^{2}+8\lambda ^{1}+\lambda ^{1-1}$$

Subtract 1 from 1.

$$-3\lambda ^{2}+8\lambda ^{1}+\lambda ^{0}$$

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

$$-3\lambda ^{2}+8\lambda +\lambda ^{0}$$

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

$$-3\lambda ^{2}+8\lambda +1$$

Evaluate

$$2+\lambda +4\lambda ^{2}-\lambda ^{3}$$