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

1 Answer

Alan P. · Jim H

Dec 28, 2016

$0$ $color(green)(0)$

Explanation:

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

For the case $f (x) = - \frac{1}{2} + \frac{7}{5} x^{3}$ $f(x)=-1/2+7/5x^3$

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
$color(white)("XXX")f'(0)=21/5 * (0)^2 =0$

enter image source here

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