Let f be a function such that f(-1) = 3 and f'(-1) = 5.
Let g be the function g(x) = 2x^3.
Let F be a function defined as F(x) = f(x) / g(x).
F'(-1) = [ ]

Question

Let f be a function such that f(-1) = 3 and f'(-1) = 5. Let g be the function g(x) = 2x^3. Let F be a function defined as F(x) = f(x) / g(x). F'(-1) = [ ]

SnapAndSolve AI · Accepted Answer

To find F'(-1), we use the quotient rule for derivatives. The quotient rule states that if F(x) = f(x) / g(x), then:

F'(x) = (g(x)f'(x) - f(x)g'(x)) / (g(x))^2

Given:

f(-1) = 3
f'(-1) = 5
g(x) = 2x^3, so g(-1) = 2(-1)^3 = -2
g'(x) = 6x^2, so g'(-1) = 6(-1)^2 = 6

Substitute these values into the quotient rule:

F'(-1) = ((-2)(5) - (3)(6)) / ((-2)^2)

F'(-1) = (-10 - 18) / 4

F'(-1) = -28 / 4

F'(-1) = -7

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Let f be a function such that f(-1) = 3 and f'(-1) = 5. Let g be the function g(x) = 2x^3. Let F be a...

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