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*) = *x*^{3 }− 12*x*^{2 }+ 21*x *+ 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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