How do you find the Slope of the curve $y = \sqrt{x}$ $y=sqrt(x)$ at the point where $x = 4$ $x=4$ ?

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Answer 1 · 2014-08-26T13:43:26

The slope of the curve $y = f (x)$ $y=f(x)$ at $x = a$ $x=a$ is $f'(a)$ .
Let us look at the posted problem.

By rewriting the square-root as 1/2-power,
$f(x)=sqrt{x}=x^{1/2}$

By the power rule,
$f'(x)=frac{1}{2}x^{-1/2}=frac{1}{2sqrt{x}}$

By plugging in $x=4$ ,
Slope: $m=f'(4)=frac{1}{2sqrt{4}}=frac{1}{4}$

Hence, the slope is $1/4$ .

I hope that this helps.

How do you find the Slope of the curve y=sqrt(x)y=√xy=sqrt(x) at the point where x=4x=4x=4?