Question

If f(x) = x^3 find df/dx | x= -5

Answer 1

75

Explanation:

So we have:

`f(x)=x^3`

Take the derivative of the function. Use the power rule, which states that:

`(d)/(dx)(x^n)=nx^(n-1)`

Therefore:

`(d)/(dx)[f(x)]=(d)/(dx)[x^3]`

Use power rule:

`(df)/(dx)=3x^2`

Now, substitute in -5:

`3(-5)^2`

Square and multiply:

`=3(25)=75`

So our answer is 75.

This means that the slope of the line tangent to the point (-5,-125) on the graph x^3 is 75.

And we're done!