# 1) Find all the values of x { f(x)=x^3 - 5x^2 - 9x + 11 } 2) Find the derivative { y=...

## Question:

1) Find all the values of x

{eq}f(x)=x^3 - 5x^2 - 9x + 11 {/eq}

2) Find the derivative

{eq}y= \frac{8}{x^4} - \frac{7}{ x^3} + \frac{ 8}{x} + \sqrt{5} {/eq}

## Derivative:

The derivative of the constant function is 0 and to solve the problem we will use the power rule where we will decrease the power of x by 1 and times it by the same decreased power.

To find the derivative of the function we will use the power rule:

{eq}\frac{\mathrm{d} x^{n}}{\mathrm{d} x}=nx^{n-1} {/eq}

Now let us write the function:

{eq}f(x)=\frac{8}{x^{4}}-\frac{7}{x^{3}}+\frac{8}{x}+\sqrt{5} {/eq}

After differentiating we get:

{eq}f'(x)=\frac{-32}{x^{5}}+\frac{21}{x^{4}}-\frac{8}{x^{2}} {/eq}