4. Find the intervals in which the function f given by f ( x) = 2x ^2 - 3 x is  (a) increasing

Answers (1)

f ( x) = 2x ^2 - 3 x
f^{'}(x) = 4x - 3
Now,
   f^{'}(x) = 0
 4x - 3 = 0
     x = \frac{3}{4}

So, the range is  \left ( -\infty, \frac{3}{4} \right ) \ and \ \left ( \frac{3}{4}, \infty \right )
So,
        f(x)< 0   when  x \ \epsilon \left ( -\infty,\frac{3}{4} \right )        Hence, f(x) is strictly decreasing in this range
and
      f(x) > 0     when  x \epsilon \left ( \frac{3}{4},\infty \right )             Hence, f(x) is strictly increasing in this range
Hence, f ( x) = 2x ^2 - 3 x   is strictly increasing in   x \epsilon \left ( \frac{3}{4},\infty \right )

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