`f(x) = -1/2 + (7/5)x^3, (0,-1/2)` Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results.

Expert Answers
kalau eNotes educator| Certified Educator

Take the derivative for the derivative function.

`f'(x)= 21/5 x^2`

Substitute the point where x=0 to find the slope at that point.

`f'(x)= 21/5 (0)^2= 0`

The slope at that point is zero.

Graph the original function.

Graph the derivative function.

We can then see that we have a horizontal slope at x=0.