Question

(Derivadas)- SOCORRO! Por favor me ajudem

Answer 1

Resposta:

a) y = - x + 2

b) y = x/9

c) y = √2(x/2 - 22)

Explicação passo-a-passo:

a)

f(2) = 2² - 5 . 2 + 6

f(2) = 4 - 10 + 6

f(2) = 10 - 10

f(2) = 0

mt = f'(x) = 2x - 5

mt = f'(2) = 2 . 2 - 5

mt = f'(2) = 4 - 5

mt = f'(2) = - 1

y - yo = m(x - x0)

y - 0 = - (x - 2)

y = - x + 2

b)

f(3) = (3 - 1)/(3 + 3)

f(3) = 2/6

f(3) = 2/2 . 1/3

f(3) = 1/3

mt = f'(x) = [(x - 1)'(x + 3) - (x - 1)(x + 3)']/(x + 3)²

mt = f'(x) = [(x + 3) - (x - 1)]/(x + 3)²

mt = f'(x) = (3 + 1)/(x + 3)²

mt = f'(x) = 4/(x + 3)²

mt = f'(3) = 4/(3 + 3)²

mt = f'(3) = 4/6²

mt = f'(3) = 4/36

mt = f'(3) = 1/9

y - y0 = m(x - x0)

y - 1/3 = 1/9(x - 3)

y - 1/3 = x/9 - 1/3

y = x/9

c)

f(45) = sen45

f(45) = √2/2

mt = f'(x) = senx'

mt = f'(x) = cosx

mt = f'(45) = cos45

mt = f'(45) = √2/2

y - yo = m(x - x0)

y - √2/2 = √2/2(x - 45)

y - √2/2 = x√2/2 - 45√2/2

y = x√2/2 - 45√2/2 + √2/2

y = x√2/2 - 44√2/2

y = x√2/2 - 22√2

y = √2(x/2 - 22)