Question
Asked Nov 5, 2019
Exercise 3: Find A and B given that the derivative f'(r) is everywhere continuous, and
Aa2 Bx 2, x<2
Br2-A
f(a)
x 2
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Exercise 3: Find A and B given that the derivative f'(r) is everywhere continuous, and Aa2 Bx 2, x<2 Br2-A f(a) x 2

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Expert Answer

Step 1

The function f(x) whose derivative is everywhere continuous is given by,

Ах? + Вх+ 2
х<2
Sк)-
| Вx* - А
х>2
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Ах? + Вх+ 2 х<2 Sк)- | Вx* - А х>2

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Step 2

The values of A and B are comput...

lim f(x)lim f (x)= f(2) = Ax2 +Bx
2 = A(2) B(2)+2 4.4 2B 2
x 2
x 2
/(x)= lim f(x)= f(2) = Bx2 - A =B(2)- A-
В
4B - A
x+2
x 2
4A+2B 24B - A
(1)
lim f'(x) im f" (x) = f(2) = 2.4x+ B = 44+2
5A 2B 2 0
x--2
x 2
lim f'(x)lm f'(x)= f(2) 2Bx = 4B
x 2
x2
4A 2 4B
(2)
4A -4B 2
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lim f(x)lim f (x)= f(2) = Ax2 +Bx 2 = A(2) B(2)+2 4.4 2B 2 x 2 x 2 /(x)= lim f(x)= f(2) = Bx2 - A =B(2)- A- В 4B - A x+2 x 2 4A+2B 24B - A (1) lim f'(x) im f" (x) = f(2) = 2.4x+ B = 44+2 5A 2B 2 0 x--2 x 2 lim f'(x)lm f'(x)= f(2) 2Bx = 4B x 2 x2 4A 2 4B (2) 4A -4B 2

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