Question

Find the intervals in which the function f given by f ( x ) = 2 x 2 − 3 x is (a) strictly increasing (b) strictly decreasing

Answer 1

The given function is f( x )=2 x 2 −3x.

Differentiate the function with respect to x.

f ′ ( x )=4x−3

Substitute f ′ ( x ) = 0 to obtain the point of maxima or minima.

f ′ ( x )=0 4x−3=0 x= 3 4

Now, the point 3 4 divides the real line in two different intervals given by,

(a)

In the interval ( −∞, 3 4 ),

f ′ ( x )<0 4x−3<0

Thus, f( x ) is strictly decreasing in the interval ( −∞, 3 4 ).

(b)

In the interval ( 3 4 ,∞ ),

f ′ ( x )>0 4x−3>0

Thus, f( x ) is strictly increasing in the interval ( 3 4 ,∞ ).