Answer:
75
Step-by-step explanation:
So we have:
[tex]f(x)=x^3[/tex]
Take the derivative of the function. Use the power rule, which states that:
[tex]\frac{d}{dx}(x^n)=nx^{n-1}[/tex]
Therefore:
[tex]\frac{d}{dx}[f(x)]=\frac{d}{dx}[x^3][/tex]
Use power rule:
[tex]\frac{df}{dx}=3x^2[/tex]
Now, substitute in -5:
[tex]3(-5)^2[/tex]
Square and multiply:
[tex]=3(25)=75[/tex]
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!
