Find the minimum or maximum value of the function y=9x2+7. Describe the domain and range of the function, and where the function is increasing and decreasing. The minimum value is Response area. The domain is Response area and the range is Response area. The function is decreasing to the Response area of x= Response area and increasing to the Response area of x= Response area.

The given function is .

Minimum or maximum value:

At the extremum (maximum or minimum) value, the function will have zero slope. So, differentiate the given function once and equate it to zero to get the extremum point.

dy/dx=0

Now, check whether the point x=0 is corresponding to the maximum value or minimum value by differentiating the function twice,

As for all value of x, so x=0 is the point corresponding to minima.

Put x=0 in the given function to get the minimum value.

Domain and range:

The function defined for all the values of the independent variable, x.

So, the domain is .

The range of the function is the possible value of y.

The minimum value, for x=0, is y=7.

The maximum value, as .

Hence the range of the function is .

The value of x for which the function is increasing and decreasing:

If the slope of the function is negative than the function is decreasing, so

Then, from equation (i), the value of x for which dy/dx<0,

18x<0

Hence, the function is decreasing for .

While if the slope of the function is positive than the function is increasing, so

Then, from equation (i), the value of x for which dy/dx<0,

18x>0

Hence, the function is increasing for