`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.
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.