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PolarNik [594]
3 years ago
15

How would I find the Max/min of this function f(x) = 2x squared +18x +16

Mathematics
1 answer:
slamgirl [31]3 years ago
7 0
F(x)=2x²+18x+16
1) we have to calculate the first derived.

f´(x)=4x+18

2) Now, we equalize the first derived to "0" and find out the value of "x"
4x+18=0
4x=-18
x=-18/4=-4.5

3)we calculate the second derived
f´´(x)=4>0  ⇒we have a minimum at x=-4.5

4) Now we calculate the value of "y".
f(-4.5)=2(-4.5)²+18(-4.5)+16=40.5-81+16=-24.5

Therefore; Exist a minimum at (-4.5 , -24.5)
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Help! I'm so confused
sweet-ann [11.9K]
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5 0
3 years ago
Solve each inequality, and then drag the correct solution graph to the inequality.
Nesterboy [21]

The correct solution graph to the inequalities are

4(9x-18)>3(8x+12)  →  C

-\frac{1}{3}(12x+6) \geq -2x +14  → A

1.6(x+8)\geq 38.4  →  B

(NOTE: The graphs are labelled A, B and C from left to right)

For the first inequality,

4(9x-18)>3(8x+12)

First, clear the brackets,

36x-72>24x+36

Then, collect like terms

36x-24x>36+72\\12x >108

Now divide both sides by 12

\frac{12x}{12} > \frac{108}{12}

∴ x > 9

For the second inequality

-\frac{1}{3}(12x+6) \geq -2x +14

First, clear the fraction by multiplying both sides by 3

3 \times[-\frac{1}{3}(12x+6)] \geq3 \times( -2x +14)

-1(12x+6) \geq -6x +42

Now, open the bracket

-12x-6 \geq -6x +42

Collect like terms

-6 -42\geq -6x +12x

-48\geq 6x

Divide both sides by 6

\frac{-48}{6} \geq \frac{6x}{6}

-8\geq x

∴ x\leq  -8

For the third inequality,

1.6(x+8)\geq 38.4

First, clear the brackets

1.6x + 12.8\geq 38.4

Collect likes terms

1.6x \geq 38.4-12.8

1.6x \geq 25.6

Divide both sides by 1.6

\frac{1.6x}{1.6}\geq  \frac{25.6}{1.6}

∴ x \geq  16

Let the graphs be A, B and C from left to right

The first graph (A) shows x\leq  -8 and this matches the 2nd inequality

The second graph (B) shows x \geq  16 and this matches the 3rd inequality

The third graph (C) shows x > 9 and this matches the 1st inequality

Hence, the correct solution graph to the inequalities are

4(9x-18)>3(8x+12)  →  C

-\frac{1}{3}(12x+6) \geq -2x +14  → A

1.6(x+8)\geq 38.4  →  B

Learn more here: brainly.com/question/17448505

8 0
2 years ago
Help me with this Promble
Alex73 [517]
5: 11.97
6: 4.1
7: 14.484
8: 12.34
Hope this helps!

8 0
3 years ago
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