Question

Use a graphing utility to approximate (to two decimal places) any relative

Answer 1

Answer:

Relative minima at $(-\frac{7}{2} , -\frac{49}{4} )$, 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.

$y= x^{2} +7x = (x + \frac{7}{2} )^{2} -\frac{49}{4}$

⇒ $y+ \frac{49}{4} = (x + \frac{7}{2} )^{2}$

Now, this is an equation of parabola having vertex at $(-\frac{7}{2} , -\frac{49}{4} )$ and the axis is parallel to positive Y-axis.

Therefore, the function(1) has a relative minima at $(-\frac{7}{2} , -\frac{49}{4} )$, and the relative maxima DNE. (Answer)