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Find the slope of the tangent line to the graph of { f(x)=\sqrt{(x)} } at x=a.

Question:

Find the slope of the tangent line to the graph of {eq}f(x)=\sqrt{(x)} {/eq} at x=a.

slope of a function

For a curve, we get the slope at a point by derivating the curve across that point

In implicit function, we see y as an implicit function of x.

The process of finding the derivative of a dependent variable in an implicit function by

differentiating each term separately is the main principle in implicit differentiation.

The slope o fa function {eq}\displaystyle y = f(x) {/eq} is obtained by derivating the f(x) with respect to x.

Answer and Explanation:

Given curve is {eq}\displaystyle f(x)=\sqrt{(x)} \\ {/eq}

Now we perform differentiation, in this case, to find out {eq}\displaystyle \frac{dy}{dx} {/eq}

So on differentiation with respect to x

{eq}\displaystyle \begin{align} f(x)=\sqrt{(x)} \\ \frac{dy}{dx} &= \frac{1}{2\sqrt{x}}\\ \text{Substitue point x = a,}\\ \frac{dy}{dx} &= \frac{1}{2\sqrt{a}} = slope\\ \end{align} {/eq}


Learn more about this topic:

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Calculating the Slope of a Line: Point-Slope Form, Slope-Intercept Form & More

from Geometry: High School

Chapter 12 / Lesson 5
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