Solve 2x^3-9x^2-24+1

$$2 { x }^{ 3 } -9 { x }^{ 2 } -24+1$$

Differentiate w.r.t. x

$$6x\left(x-3\right)$$

Steps Using Derivative Rule for Sum

Add -24 and 1 to get -23.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}-9x^{2}-23)$$

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}.

$$3\times 2x^{3-1}+2\left(-9\right)x^{2-1}$$

Multiply 3 times 2.

$$6x^{3-1}+2\left(-9\right)x^{2-1}$$

Subtract 1 from 3.

$$6x^{2}+2\left(-9\right)x^{2-1}$$

Multiply 2 times -9.

$$6x^{2}-18x^{2-1}$$

Subtract 1 from 2.

$$6x^{2}-18x^{1}$$

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

$$6x^{2}-18x$$

Evaluate

$$2x^{3}-9x^{2}-23$$

Solution Steps

Add -24 and 1 to get -23.

$$2x^{3}-9x^{2}-23$$