Solve f(x)=-2x^3+15x^2+40x-150

$$f ( x ) = - 2 x ^ { 3 } + 15 x ^ { 2 } + 40 x - 150$$

Differentiate w.r.t. x

$$40+30x-6x^{2}$$

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}.

$$3\left(-2\right)x^{3-1}+2\times 15x^{2-1}+40x^{1-1}$$

Multiply 3 times -2.

$$-6x^{3-1}+2\times 15x^{2-1}+40x^{1-1}$$

Subtract 1 from 3.

$$-6x^{2}+2\times 15x^{2-1}+40x^{1-1}$$

Multiply 2 times 15.

$$-6x^{2}+30x^{2-1}+40x^{1-1}$$

Subtract 1 from 2.

$$-6x^{2}+30x^{1}+40x^{1-1}$$

Subtract 1 from 1.

$$-6x^{2}+30x^{1}+40x^{0}$$

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

$$-6x^{2}+30x+40x^{0}$$

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

$$-6x^{2}+30x+40\times 1$$

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

$$-6x^{2}+30x+40$$

Evaluate

$$-2x^{3}+15x^{2}+40x-150$$