Question

What are the maximum and minimum of the function f(x) = 0.9 I -(x - 5) I + 7 ? A. Maximum at (5,7) and minimum at (0,0) B. Minimum at (5,7) and no maximum C. Minimum at (0,0) and no maximum D. Maximum at (5,7) and no minimum

Answer 1

Answer:

$Minimum = (5,7)$

No maximum

Step-by-step explanation:

Given

$f(x) = 0.9|-(x - 5)| + 7$

Solving (a): The minimum

The minimum is when the absolute parameter gives 0

i.e.

$0.9|-(x - 5)| =0$

Divide both sides by 0.9

$|-(x - 5)| =0$

Open bracket

$|-x + 5| =0$

Remove absolute sign

$-x + 5 =0$

Collect like terms

$x = 5$

Then the y value is:

$f(x) = 0.9|-(x - 5)| + 7$

Recall that: $0.9|-(x - 5)| =0$

So, we have:

$f(x) = 0 + 7$

$f(x) = 7$

Hence, the minimum is at: $(5,7)$

Since the minimum is at $(5,7)$, then the graph will open upwards.

Hence. the function has no maximum; i.e.

$Maximum = (\infty,\infty)$