The function f defined by f(x) = x3 - 3x2 + 5x + 7 , is :

Question

The function f defined by

f(x) = x3 - 3x2 + 5x + 7 , is :

Accepted Answer

The given function is

$f(x) = {x^2} - 3{x^2} + 5x + 7$

$f'(x) = 3{x^2} - 6x + 5$

The discriminant of the above quadratic equation is

$$\Delta  = 36 - 4(3)(5) = 36 - 60  0\,\forall x \in {R^ + }$$

Also, $$f'(x) > 0\,\forall x \in {R^ - }$$

Therefore, the given function f is increasing in R.

Solutions · 1