Solve f(x)=6x^3-30x^2-48x+1

$$f ( x ) = 6 x ^ { 3 } - 30 x ^ { 2 } - 48 x + 1$$

Differentiate w.r.t. x

$$6\left(x-4\right)\left(3x+2\right)$$

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}.

$$3\times 6x^{3-1}+2\left(-30\right)x^{2-1}-48x^{1-1}$$

Multiply 3 times 6.

$$18x^{3-1}+2\left(-30\right)x^{2-1}-48x^{1-1}$$

Subtract 1 from 3.

$$18x^{2}+2\left(-30\right)x^{2-1}-48x^{1-1}$$

Multiply 2 times -30.

$$18x^{2}-60x^{2-1}-48x^{1-1}$$

Subtract 1 from 2.

$$18x^{2}-60x^{1}-48x^{1-1}$$

Subtract 1 from 1.

$$18x^{2}-60x^{1}-48x^{0}$$

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

$$18x^{2}-60x-48x^{0}$$

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

$$18x^{2}-60x-48$$

Evaluate

$$6x^{3}-30x^{2}-48x+1$$