Answer
The derivative at the point $(0, -(\frac{1}{2}))$ is 0.
Work Step by Step
The function $-\frac{1}{2}+\frac{7}{5}x^3$ is the sum of "smaller" functions hence the overall derivative is the sum of the derivative of the smaller functions.
The derivative of $-\frac{1}{2}$ is 0. The derivative of $\frac{7}{5}x^3$ is $(\frac{7}{5})(3)x^{3-1}$ which when simplified is equal to $\frac{21}{5}x^2$; hence, the overall derivative is $\frac{21}{5}x^2$.
To evaluate the derivative substitute in the x-coordinate. Plugging in 0 gives us $(\frac{21}{5})(0)$ which is 0.
