Answer:
Relative minima at [tex](-\frac{7}{2} , -\frac{49}{4} )[/tex], and relative maxima DNE.
Step-by-step explanation:
The given function is f(x) = x (x + 7) ...... (1)
We have to calculate the relative maxima and relative minima at point (x, y).
Rearranging the function given above we get.
[tex]y= x^{2} +7x = (x + \frac{7}{2} )^{2} -\frac{49}{4}[/tex]
⇒ [tex]y+ \frac{49}{4} = (x + \frac{7}{2} )^{2}[/tex]
Now, this is an equation of parabola having vertex at [tex](-\frac{7}{2} , -\frac{49}{4} )[/tex] and the axis is parallel to positive Y-axis.
Therefore, the function(1) has a relative minima at [tex](-\frac{7}{2} , -\frac{49}{4} )[/tex], and the relative maxima DNE. (Answer)
