Solve f^prime(x)=6x-8text{en}(1,2)

$$f ^ { \prime } ( x ) = 6 x - 8 \text { en } ( 1,2 )$$

Solve for n

$$n=\frac{5x}{8e}$$

Steps for Solving Linear Equation

Multiply 8 and 1,2 to get 9,6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(f)x=6x-9,6en$$

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

$$6x-9,6en=\frac{\mathrm{d}}{\mathrm{d}x}(f)x$$

Subtract 6x from both sides.

$$-9,6en=\frac{\mathrm{d}}{\mathrm{d}x}(f)x-6x$$

The equation is in standard form.

$$\left(-\frac{48e}{5}\right)n=-6x$$

Divide both sides by -9,6e.

$$\frac{\left(-\frac{48e}{5}\right)n}{-\frac{48e}{5}}=-\frac{6x}{-\frac{48e}{5}}$$

Dividing by -9,6e undoes the multiplication by -9,6e.

$$n=-\frac{6x}{-\frac{48e}{5}}$$

Divide -6x by -9,6e.

$$n=\frac{5x}{8e}$$

Solve for f

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

$$x=\frac{8en}{5}$$