To find the value of g′(1), we can use the formula for the derivative of an inverse function, which is 1/f′(g(1)).

First, we need to find the derivative of f(x), which is f′(x). The function f(x) = x^3 + 4x + 1, so its derivative f′(x) = 3x^2 + 4.

Next, we substitute g(1) into f′(x). Since g is the inverse function of f, g(1) is the value of x such that f(x) = 1. From the given, we know that g(1) = 0.

So, f′(g(1)) = f′(0) = 3*0^2 + 4 = 4.

Finally, we substitute this into the formula for the derivative of an inverse function to get g′(1) = 1/f′(g(1)) = 1/4.

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To find the value of g′(1), we can use the formula for the derivative of an inverse function, which is 1/f′(g(1)).

First, we need to find the derivative of f(x), which is f′(x). The function f(x) = x^3 + 4x + 1, so its derivative f′(x) = 3x^2 + 4.

Next, we substitute g(1) into f′(x). Since g is the inverse function of f, g(1) is the value of x such that f(x) = 1. From the given, we know that g(1) = 0.

So, f′(g(1)) = f′(0) = 3*0^2 + 4 = 4.

Finally, we substitute this into the formula for the derivative of an inverse function to get g′(1) = 1/f′(g(1)) = 1/4.

Knowee AI · Accepted Answer

To find the value of g′(1), we can use the formula for the derivative of an inverse function, which is 1/f′(g(1)).

First, we need to find the derivative of f(x), which is f′(x). The function f(x) = x^3 + 4x + 1, so its derivative f′(x) = 3x^2 + 4.

Next, we substitute g(1) into f′(x). Since g is the inverse function of f, g(1) is the value of x such that f(x) = 1. From the given, we know that g(1) = 0.

So, f′(g(1)) = f′(0) = 3*0^2 + 4 = 4.

Finally, we substitute this into the formula for the derivative of an inverse function to get g′(1) = 1/f′(g(1)) = 1/4.

The function ff is defined by f, of, x, equals, x, cubed, plus, 4, x, plus, 1, .f(x)=x 3 +4x+1. If gg is the inverse function of ff and g, of, 1, equals, 0, commag(1)=0, what is the value of g, prime, of, 1, question markg ′ (1)?

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