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

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

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best_answer

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 is strictly increasing in   x \epsilon \left ( \frac{3}{4},\infty \right ).

Posted by

Gautam harsolia

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