Question

Find the interval in which the function f(x)=(x+7)^4+4 is increasing. (Use symbolic notation and fractions where needed. Give your answers as intervals in the form (∗,∗). Use the symbol [infinity] ff infinity, U for combining intervals, and the appropriate type of parenthesis "(". ")", "[" or "]" depending on whether the inte is open or closed.)

Answer 1

To find the interval in which the function is increasing, differentiate the function, set the derivative equal to zero, solve for x, and determine the intervals where the derivative is positive.

Step-by-step explanation:

To find the interval in which the function f(x)=(x+7)^4+4 is increasing, we need to determine the values of x for which the derivative of the function is positive. First, we differentiate the function: f'(x) = 4(x+7)^3. Now, we set the derivative equal to zero and solve for x:

4(x+7)^3 = 0

(x+7)^3 = 0

x = -7

Since the derivative is positive for values of x greater than -7, we can conclude that the function is increasing in the interval (-7, infinity).

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