แบบฝึกหัดที่ 1 สูตร m=slope = f'(x₁) - lim m=slope = f'(x) - lim สมการเส้นตรง y = mx+c 15 HO X x-2 3 (28) f(xo+h)-f(x) h In Exercises 11-18, find the slope of the function's graph at the given point. Then find an equation for the line tangent to the graph there. 11. f(x) = x² + 1, (2,5) 12. f(x) = x - 2x², (1,-1) 13. g(x) 14. g(x)= " f(x +h)-f(x) h (3, 3) ที่จุด x = x0 จุดx ใด ๆ 16 160 8 ²¹ (2, 2) 326 (1 1) Finding Derivative Functions and Values Using the definition, calculate the derivatives of the functions in Exer- cises 1-6. Then find the values of the derivatives as specified. 1. f(x)-4-x²; f(-3), f'(0), f'(1) 2. F(x) = (x − 1)² + 1; F(-1), F(0), F'(2) 3. g (1) g'(-1),g'(2).g'(√3) 4. k(z) = ¹2,²; K'(-1), k'(1), K'(√₂) 5. p(0) V30; p'(1),p'(3),p'(2/3) In Exercises 7-12, find the indicated derivatives. dy y = 2x³ 7. 9. 11. dp dq if s = if p = 2t + 1 8. if r= $³25² +3 ds dv 10. 12. dw if v = t - if z = 3w
แบบฝึกหัดที่ 1 สูตร m=slope = f'(x₁) - lim m=slope = f'(x) - lim สมการเส้นตรง y = mx+c 15 HO X x-2 3 (28) f(xo+h)-f(x) h In Exercises 11-18, find the slope of the function's graph at the given point. Then find an equation for the line tangent to the graph there. 11. f(x) = x² + 1, (2,5) 12. f(x) = x - 2x², (1,-1) 13. g(x) 14. g(x)= " f(x +h)-f(x) h (3, 3) ที่จุด x = x0 จุดx ใด ๆ 16 160 8 ²¹ (2, 2) 326 (1 1) Finding Derivative Functions and Values Using the definition, calculate the derivatives of the functions in Exer- cises 1-6. Then find the values of the derivatives as specified. 1. f(x)-4-x²; f(-3), f'(0), f'(1) 2. F(x) = (x − 1)² + 1; F(-1), F(0), F'(2) 3. g (1) g'(-1),g'(2).g'(√3) 4. k(z) = ¹2,²; K'(-1), k'(1), K'(√₂) 5. p(0) V30; p'(1),p'(3),p'(2/3) In Exercises 7-12, find the indicated derivatives. dy y = 2x³ 7. 9. 11. dp dq if s = if p = 2t + 1 8. if r= $³25² +3 ds dv 10. 12. dw if v = t - if z = 3w
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
Transcribed Image Text:แบบฝึกหัดที่ 1
สูตร
m=slope = f'(x) = lim
A0
m = slope = f'(x) - lim
สมการเส้นตรง y = mx+c
f(xo+h)-f(xo)
h
f(x+h)-f(x)
h
In Exercises 11-18, find the slope of the function's graph at the given
point. Then find an equation for the line tangent to the graph there.
11. f(x) = x² + 1, (2,5)
2x², (1,-1)
12. f(x) = x
8
x²
14. g(x) =
(2, 2)
16. h(t) = t³ + 3t, (1,4)
18. f(x) = √x + 1, (8,3)
13. g(x)=x₂, (3, 3)
15. h(t) = 1³, (2,8)
17. f(x)=√x, (4,2)
21. y =
ñanx = xo
ที่จุดx ใด ๆ
In Exercises 19-22, find the slope of the curve at the point indicated.
19. y = 5x², x = -1
20. y
1x²,
x = 2
x = 3
x = 0
22. y =
x 1
x+1'
Finding Derivative Functions and Values
Using the definition, calculate the derivatives of the functions in Exer-
cises 1-6. Then find the values of the derivatives as specified.
1. f(x) = 4x²; f'(-3), f'(0), f'(1)
2. F(x) = (x 1)² + 1; F(-1), F'(0), F'(2)
3. g(t);g'(-1), g'(2), g'(√3)
-1-²; K'(-1), K(1), K(√2)
2z'
5. p(0) = √30; p'(1),p'(3),p'(2/3)
In Exercises 7-12, find the indicated derivatives.
dr
7. if y = 2r³
8. if r83 25² +3
dx
ds
du
4. k(z) =
9.
11.
dq
if s=
if p=
1
23. f(x) =
Vq
25. g(x) =
10.
12.
x-1
dw
if
Using the Alternative Formula for Derivatives
Use the formula
f'(x) = lim
if
v = t
z =
to find the derivative of the functions in Exercises 23-26.
1
x + 2
24. f(x)=x²-3x + 4
26. g(x) = 1 + √x
f(z)-f(x)
Z-x
1
√3w
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