find the slope of the graph of the function at the given point. use\nfunction point\n$f(x)=-\frac{1}{4}+\frac…

find the slope of the graph of the function at the given point. use\nfunction point\n$f(x)=-\frac{1}{4}+\frac{7}{6}x^{3}$, $(0,-\frac{1}{4})$ \n$f(0)=$

find the slope of the graph of the function at the given point. use\nfunction point\n$f(x)=-\frac{1}{4}+\frac{7}{6}x^{3}$, $(0,-\frac{1}{4})$ \n$f(0)=$

Answer

Explanation:

Step1: Find derivative of f(x)

$f'(x) = \frac{d}{dx}\left(-\frac{1}{4} + \frac{7}{6}x^3\right) = 0 + \frac{7}{6} \cdot 3x^2 = \frac{7}{2}x^2$

Step2: Evaluate f'(x) at x=0

$f'(0) = \frac{7}{2}(0)^2 = 0$

Answer:

0