Question

How do you find the slope of the graph `f(x)=-1/2+7/5x^3` at (0,-1/2)?

Answer 1

`color(green)(0)`

Explanation:

The slope of a function `f(x)` for a non-specific point `x` is given by the derivative of the function `f(x)`.

For the case `f(x)=-1/2+7/5x^3`

the derivative (using the exponent rule) is
`color(white)("XXX")f'(x)=3xx7/5x^(3-1) = 21/5x^2`

At the point `(0,-1/2)`
`color(white)("XXX")x=0` (and `y=-1/2`, but that's irrelevant).
so the slope is
`color(white)("XXX")f'(0)=21/5 * (0)^2 =0`