Solve f^prime(x)=x^2-x-3a

$$f ^ { \prime } ( x ) = x ^ { 2 } - x - 3 a$$

Solve for a

$$a=-\frac{x\left(1-x\right)}{3}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-x-3a=\frac{\mathrm{d}}{\mathrm{d}x}(f)x$$

Subtract x^{2} from both sides.

$$-x-3a=\frac{\mathrm{d}}{\mathrm{d}x}(f)x-x^{2}$$

Add x to both sides.

$$-3a=\frac{\mathrm{d}}{\mathrm{d}x}(f)x-x^{2}+x$$

The equation is in standard form.

$$-3a=x-x^{2}$$

Divide both sides by -3.

$$\frac{-3a}{-3}=\frac{x\left(1-x\right)}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$a=\frac{x\left(1-x\right)}{-3}$$

Divide x\left(1-x\right) by -3.

$$a=-\frac{x\left(1-x\right)}{3}$$

Solve for f

$$f\in \mathrm{R}$$

$$a=-\frac{x\left(1-x\right)}{3}$$