Solve f^prime(T)=e^frac{2{3}x}(1-x/2)

$$f ^ { \prime } ( T ) = e ^ { \frac { 2 } { 3 } x } ( 1 - \frac { x } { 2 } )$$

Solve for T

$$T\in \mathrm{R}$$

$$x=2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2\frac{\mathrm{d}}{\mathrm{d}x}(f)T=2e^{\frac{2}{3}x}\left(1-\frac{x}{2}\right)$$

Use the distributive property to multiply 2e^{\frac{2}{3}x} by 1-\frac{x}{2}.

$$2\frac{\mathrm{d}}{\mathrm{d}x}(f)T=2e^{\frac{2}{3}x}+2e^{\frac{2}{3}x}\left(-\frac{x}{2}\right)$$

Express 2\left(-\frac{x}{2}\right) as a single fraction.

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

Cancel out 2 and 2.

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

The equation is in standard form.

$$0=2e^{\frac{2x}{3}}-xe^{\frac{2x}{3}}$$

This is false for any T.

$$T\in$$

Solve for f

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

$$x=2$$