009A Sample Midterm 1, Problem 3

Let $y={\sqrt {3x-5}}.$

a) Use the definition of the derivative to compute ${\frac {dy}{dx}}$ for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=\sqrt{3x-5}.}

b) Find the equation of the tangent line to $y={\sqrt {3x-5}}$ at Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (2,1).}

Foundations:
1. Limit Definition of Derivative
2. Tangent line equation

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

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