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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 3.1 - Problem 50e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 3.1 - Problem 50e

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# Solved: Calculating derivatives f(x+h)f(x) a. or the ISBN: 9780321570567 2

## Solution for problem 50E Chapter 3.1

Calculus: Early Transcendentals | 1st Edition

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Problem 50E

Calculating derivatives f(x+h)?f(x) a.?? or the following functions, find f using the definition? f (x) = lim h . h?0 b.? ?Determine an equation of the line tangent to the graph of f at? (?a?, ?f?(?a?)) ?for the given value of a. f(x) = x + 2; a = 7

Step-by-Step Solution:
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SOLUTION STEP 1 (a). Given f(x) = x+2. We need to find the derivative of f(x) using the definition of the derivative f(x+h)f(x) The definition of the derivative is(x) = lim h h0 f(x+h) = (+h)+2 (x+h)+2 x+2 Thus f (x) =h0m h To solve this we have to multiply the numerator and the denominator with the conjugate of the numerator. (x+h)+2 x+2 (x+h)+2 x+2 (x+h)+2+ x+2 Therefore f(x) = lim h = lim h × (x+h)+2+ x+2 h0 h0 =lim (x+h)+2(x+2)= lim h = h0 h (x+h)+2+ x+2 h0 h (x+h)+2+ x+2 = 1 = 1 x+2+ x+2 2 x+2 Therefore f (x) =2 x+2 STEP 2 (b). Determine an equation of the line tangent to the graph of f at (a, f(a)),{ie,(7,f(7))} for the given value a=7. Equation of a tangent line at (a,f(a)) is y y =1m(x x ) 1 Slope is the m here which is given by the equation m = f (a) = f(7) = 1 = 1 = 1 = 1 2 7+2 2 9 2×3 6 f(a) = f(7) = (7)+2 = 9 = 3 Therefore the line tangent to the graph of f at (7,3) for the given value a=7 is y3 = (x7) = x 1 7 1 67 1 6 116 y = x6 +36= x+ 6 6 The equation of the line is y = x+ 11 6 6

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##### ISBN: 9780321570567

The answer to “Calculating derivatives f(x+h)?f(x) a.?? or the following functions, find f using the definition? f (x) = lim h . h?0 b.? ?Determine an equation of the line tangent to the graph of f at? (?a?, ?f?(?a?)) ?for the given value of a. f(x) = x + 2; a = 7” is broken down into a number of easy to follow steps, and 50 words. This full solution covers the following key subjects: Calculating, definition, Derivatives, determine, equation. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The full step-by-step solution to problem: 50E from chapter: 3.1 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Since the solution to 50E from 3.1 chapter was answered, more than 299 students have viewed the full step-by-step answer.

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