Solving for a Zero Derivative

Question

Determine the value of $$x$$ for which the derivative of $$f(x)=(4*x+9)^{3/2}$$ is zero by solving $$f'(x)=0$$.
 
| Function               | Differentiation Step                                      |
|------------------------|-----------------------------------------------------------|
| $$f(x)=(4*x+9)^{3/2}$$   | $$f'(x)=\frac{3}{2}*(4*x+9)^{1/2}*4=6*(4*x+9)^{1/2}$$          |
| Set Derivative to Zero | $$6*(4*x+9)^{1/2}=0 \Rightarrow (4*x+9)^{1/2}=0$$                 |
| Solve                  | $$4*x+9=0\Rightarrow x=-\frac{9}{4}$$                            |

Accepted Answer

$$x=-\frac{9}{4}$$

Answer

$$x=-\frac{3}{2}$$

Answer

$$x=\frac{9}{4}$$

Answer

$$x=\frac{3}{2}$$

Function	Differentiation Step
$$f(x)=(4*x+9)^{3/2}$$	$$f'(x)=\frac{3}{2}(4x+9)^{1/2}4=6(4*x+9)^{1/2}$$
Set Derivative to Zero	$$6(4x+9)^{1/2}=0 \Rightarrow (4*x+9)^{1/2}=0$$
Solve	$$4*x+9=0\Rightarrow x=-\frac{9}{4}$$

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