The instantaneous slope of f(x)when f(x) is radical10A-1:8qrt(13)4,0f(x) = √4x + 5compute the instantaneous slope at: (-1, √I)Start with two pointsA: (-1, VI) and B: (−1+h, ?)What is the y-coordinate of B?• Because the a-coordinate of B depends on h, the y-coordinate will also depend on h.

Given : A : ( -1,1)x coordinate of B = -1+hy coordinate of B = 4(-1+h)+5=-4+4h+5 =4h+1

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Math

Calculus

The instantaneous slope of f(x) when f(x) is radical

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 41E

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Question

The instantaneous slope of f(x)
when f(x) is radical
10
A-1:8qrt(13)
4,0
f(x) = √4x + 5
compute the instantaneous slope at: (-1, √I)
Start with two points
A: (-1, VI) and B: (−1+h, ?)
What is the y-coordinate of B?
• Because the a-coordinate of B depends on h, the y-coordinate will also depend on h.

Expert Solution

Step 1

Given :

$\begin{array}{rcl} A : (- 1, \sqrt{1}) \\ x c o o r d i n a t e o f B & = & - 1 + h \\ y c o o r d i n a t e o f B & = & \sqrt{4 (- 1 + h) + 5} \\ = & \sqrt{- 4 + 4 h + 5} \\ = & \sqrt{4 h + 1} \end{array}$

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