Question

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

Answer 1

Answer:

75

Step-by-step explanation:

So we have:

$f(x)=x^3$

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

$\frac{d}{dx}(x^n)=nx^{n-1}$

Therefore:

$\frac{d}{dx}[f(x)]=\frac{d}{dx}[x^3]$

Use power rule:

$\frac{df}{dx}=3x^2$

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!