if x=2 , f(x)=1if x=3 , f(x)=4if x=5 , f(x)=-2if x=8 , f(x)=3if x=13 , f(x)=6f is twice variable for all real numbers. 1. Find f'(4)2. Approximate ∫213f′(x)dx2. Find the value of ∫28(3−f′(x))dx

1. f′(4)=f(5)−f(3)5−3=(-2-4)/2=-32. The lengths of intervals are 1, 2, 3, and 5 respectively. Right end points:x1=3,x2=5,x3=8,x4=13Use Riemann Sum:R4=f(3)×1+f(5)×2+f(8)×3+f(13)×5R4=4−2×2+3×3+6×5R4=393. (C)∫28(3−f′(x))dx=[3x−f(x)]28=3×8−f(8)−3×2+f(2)=24-3-6+1=16

Explained: "if x=2 , f(x)=1if x=3 , f(x)=4if x=5..."

High School
Geometry
Trigonometry
Trigonometric Functions

sibuzwaW

Answered question

2021-10-26

if x=2 , f(x)=1
if x=3 , f(x)=4
if x=5 , f(x)=-2
if x=8 , f(x)=3
if x=13 , f(x)=6
f is twice variable for all real numbers.
1. Find f'(4)
2. Approximate

{\int_{2}}^{13} f^{'} (x) d x

2. Find the value of

{\int_{2}}^{8} (3 - f^{'} (x)) d x

Answer & Explanation

Tuthornt

Skilled2021-10-27Added 107 answers

f^{'} (4) = \frac{f (5) - f (3)}{5 - 3}

=(-2-4)/2
=-3
2. The lengths of intervals are 1, 2, 3, and 5 respectively. Right end points:

\underset{1}{x} = 3, \underset{2}{x} = 5, \underset{3}{x} = 8, \underset{4}{x} = 13

Use Riemann Sum:

\underset{4}{R} = f (3) \times 1 + f (5) \times 2 + f (8) \times 3 + f (13) \times 5

\underset{4}{R} = 4 - 2 \times 2 + 3 \times 3 + 6 \times 5

\underset{4}{R} = 39

3. (C)

{\int_{2}}^{8} (3 - f^{'} (x)) d x = {\underset{2}{[3 x - f (x)]}}^{8}

= 3 \times 8 - f (8) - 3 \times 2 + f (2)

=24-3-6+1
=16

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