Find f'(a). f(t) = Since f(t) Step 1 To find f'(a), we will use the formula f(t) - f(a) t-a 7t + 15 t + 6 = f'(a) = lim t-a 7t + 15 t +6 we have 7t + 15 f'(a) = lim t+ 6 7t + 15 7a+ 15 t + 6 a + 6 7a + 15 a +1 t-a Putting the fractions in the numerator over a common denominator and simplifying, we have (7t+15) a+6 ✓) - (72 + (t + 6)(a + 6) 7ta + 15a + 42t +90- 7at - 15t- 42a - 90 (t + 6)(a + 6) (7a+ 15)(t + 6) ])+- ( [ (t + 6)(a + 6)
Find f'(a). f(t) = Since f(t) Step 1 To find f'(a), we will use the formula f(t) - f(a) t-a 7t + 15 t + 6 = f'(a) = lim t-a 7t + 15 t +6 we have 7t + 15 f'(a) = lim t+ 6 7t + 15 7a+ 15 t + 6 a + 6 7a + 15 a +1 t-a Putting the fractions in the numerator over a common denominator and simplifying, we have (7t+15) a+6 ✓) - (72 + (t + 6)(a + 6) 7ta + 15a + 42t +90- 7at - 15t- 42a - 90 (t + 6)(a + 6) (7a+ 15)(t + 6) ])+- ( [ (t + 6)(a + 6)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![Find f'(a).
f(t)
Since f(t) =
=
Step 1
To find f'(a), we will use the formula
f(t) = f(a)
7t + 15
t + 6
7t + 15
t + 6
f'(a) = = lim
t-a t-a
7t + 15
t + 6
we have
f'(a) = lim
t-a
7a + 15
a +6
Putting the fractions in the numerator over a common denominator and simplifying, we have
(7t+15) a +6
=
=
7t + 15
t + 6
=
7a+ 15
t-a
]₁)-(²
(t + 6)(a + 6)
7ta + 15a + 42t +90 - 7at - 15t - 42a - 90
(t + 6)(a + 6)
])-([
(t + 6)(a +6)
- (7a+ 15)(t + 6)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa69a982a-8c24-4436-975e-615a072603a1%2F1b7584f9-a9b1-4775-b8fa-8d1175fcce1f%2F73y2uer_processed.png&w=3840&q=75)
Transcribed Image Text:Find f'(a).
f(t)
Since f(t) =
=
Step 1
To find f'(a), we will use the formula
f(t) = f(a)
7t + 15
t + 6
7t + 15
t + 6
f'(a) = = lim
t-a t-a
7t + 15
t + 6
we have
f'(a) = lim
t-a
7a + 15
a +6
Putting the fractions in the numerator over a common denominator and simplifying, we have
(7t+15) a +6
=
=
7t + 15
t + 6
=
7a+ 15
t-a
]₁)-(²
(t + 6)(a + 6)
7ta + 15a + 42t +90 - 7at - 15t - 42a - 90
(t + 6)(a + 6)
])-([
(t + 6)(a +6)
- (7a+ 15)(t + 6)
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