  Let f(x)=x3−12x^2+21x+11. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima).f is increasing on intervals=f is decreasing on intervals= the relative maxima of f occur at x=the relative minima of f occur at x=

Question

Let f(x)=x3−12x^2+21x+11. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima).

f is increasing on intervals=

f is decreasing on intervals=

the relative maxima of f occur at x=

the relative minima of f occur at x=

Step 1

Given:

The function is f(x) = x3 − 12x2 + 21x + 11.

Step 2

Calculation:

The domain of the given function is (−∞, ∞).

Obtain the critical points as follows.

Differentiate the given function with respect to x .

Step 3

The signs of f’(x) are summarized ...

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