Solve f(x)=x^4-4x^3+3x^3-12x+24

$$f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 3 x ^ { 3 } - 12 x + 24$$

Differentiate w.r.t. x

$$4x^{3}-3x^{2}-12$$

Steps Using Derivative Rule for Sum

Combine -4x^{3} and 3x^{3} to get -x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}-x^{3}-12x+24)$$

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}.

$$4x^{4-1}+3\left(-1\right)x^{3-1}-12x^{1-1}$$

Subtract 1 from 4.

$$4x^{3}+3\left(-1\right)x^{3-1}-12x^{1-1}$$

Multiply 3 times -1.

$$4x^{3}-3x^{3-1}-12x^{1-1}$$

Subtract 1 from 3.

$$4x^{3}-3x^{2}-12x^{1-1}$$

Subtract 1 from 1.

$$4x^{3}-3x^{2}-12x^{0}$$

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

$$4x^{3}-3x^{2}-12$$

Evaluate

$$x^{4}-x^{3}-12x+24$$

Solution Steps

Combine -4x^{3} and 3x^{3} to get -x^{3}.

$$x^{4}-x^{3}-12x+24$$