Use the derivative function, f ' ( x ) f ′ ( x ) , to determine where the function f ( x ) = − 4 x 2 + 13 x − 7 f ( x ) = - 4 x 2 + 13 x - 7 is increasing.

Given:

The function is

To find:

The interval on which the function is increasing.

Solution:

We have,

Differentiate with respect to x.

Equate f'(x)=0.

The point x=1.625 divides the number line in two parts .

f'(x) is positive for . It means the function is increasing on this interval.

f'(x) is negative for . It means the function is decreasing on this interval.

At x=1.625, f'(x) is 0. It is turning point so it will included in both intervals.

Therefore, the function is increasing on .

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