Question

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

minima or maxima of the function. (If an answer does not exist, enter DNE.)
f(x) = x(x + 7)
relative minimum
(x, y) =
relative maximum
(x, y) =​

Answer 1

Relative minima at
`(-(7)/(2) , -(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 + (7)/(2) )^(2) -(49)/(4)`

⇒
`y+ (49)/(4) = (x + (7)/(2) )^(2)`

Now, this is an equation of parabola having vertex at
`(-(7)/(2) , -(49)/(4) )` and the axis is parallel to positive Y-axis.

Therefore, the function(1) has a relative minima at
`(-(7)/(2) , -(49)/(4) )`, and the relative maxima DNE. (Answer)