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Find an equation of the tangent line to the curve y =√x at the given point (4,2) Use the definition to find the slope of the tangent

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

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Question

Find an equation of the tangent line to the curve y =√x at the given point (4,2)

Use the definition to find the slope of the tangent.

Expert Solution

Step 1

The expression for the equation of the tangent line is:

$(y - y_{1}) = m (x - x_{1})$

Where, 'm' is the slope of the tangent line.

And

The slope of the tangent line to the given curve is equal to the derivative of the function at a given point.

$f' (x) = m$

We know that the expression for the derivative, according to the definition of the limit is:

$m = f' (x) = \lim_{h \to 0} \frac{f (x + h) - f (x)}{h}$

Given:

$y = \sqrt{x} & P (x_{1}, y_{1}) = (4, 2)$

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