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Find the critical numbers of the function.
f(x)= 3x^4+4x^3-12

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Answer: To find the critical numbers of the function, we need to find the values of x where the derivative of the function is equal to zero or does not exist.

Given function: f(x) = 3x^4 + 4x^3 - 12

Step 1: Find the derivative of the function f(x) with respect to x (f'(x)):

f'(x) = d/dx(3x^4) + d/dx(4x^3) - d/dx(12)

f'(x) = 12x^3 + 12x^2

Step 2: Set the derivative f'(x) equal to zero and solve for x to find the critical points:

12x^3 + 12x^2 = 0

Step 3: Factor out the common term 12x^2 from the equation:

12x^2(x + 1) = 0

Step 4: Set each factor equal to zero and solve for x:

12x^2 = 0

x^2 = 0

x = 0

x + 1 = 0

x = -1

So, the critical numbers of the function f(x) = 3x^4 + 4x^3 - 12 are x = 0 and x = -1.

User Carrie
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