Functions f(x) and g(x) are shown below:

Mathematics

1 answer:

kondor19780726 [428]4 years ago

4 0

We look for the minimum of each function.
For f (x) = 3x2 + 12x + 16:
We derive the function:
f '(x) = 6x + 12
We match zero:
6x + 12 = 0
We clear the value of x:
x = -12/6
x = -2
We substitute the value of x in the equation:
f (-2) = 3 * (- 2) ^ 2 + 12 * (- 2) + 16
f (-2) = 4
For g (x) = 2sin(x-pi):
From the graph we observe that the minimum value of the function is:
y = -2
Answer:
A function that has the smallest minimum y-value is:
y = -2

You might be interested in

THE GRAPH IS BELOW THANKS :) Anika is on the crew to set up rides for the state fair. The crew does most of the setup on the day

Vaselesa [24]

Answer:

(a) We will form an equation of line from the points given (6,10) and (2,15)

Using: $y-y_1=\frac{y_2-y_1}{x_2-x_1}\cdot (x-x_1)$

On substituting the values in the formula above we will get the required equation of line.

$y-10=\frac{15-10}{2-6}\cdot (x-6)$

$\Rightarrow y-10=\frac{5}{-4}\cdot (x-6)$

On simplification we will get:

$y=\frac{1}{4}(-5x+70)$

(b) We need to tell at day 0 put x=0 in above equation:

$y=\frac{1}{4}(-5\cdot 0+70)$

$y=70$

Anika worked for 70 hours on the set up crew on the day the fair arrived at the fairgrounds day 0.

Now, we need to tell decrease per day which is equal to the slope of line

To find the slope compare the equation with general equation which is y=mx+c where m is slope

Here, in $y=\frac{1}{4}(-5x+70)$

$m=\frac{-5}{4}$ which is the decrease per day.

3 0

3 years ago

There are 9 more pencils then pens in a container. There are 25 writing utensils in the container in all. How many pens are ther

VashaNatasha [74]

In order to determine the number of pens present in the container, we need to set up equations from the given in the problem statement. We do as follows:

let x the number of pencils
y the number of pens

From the statement, 9 more pencils then pens in a container,

x = y + 9

From the statement, there are 25 writing utensils in the container in all,

x + y = 25

We use substitution method to calculate for x and y,

y + 9 + y = 25
2y = 16
y = 8
x = 17

Therefore, there are 8 pens in the container and 17 pencils.

3 0

4 years ago

CAN SOMEONE HELP REALLY FAST IM ON A TIMED TEST!!!!!The volume of a cube is 64 cubic inches. Which expression represents s, the

AnnyKZ [126]

Answer:

Step-by-step explanation:

The side length would be 4, but I'm a bit confused on what the "Recall the Formula" portion is about. I'm sorry if this doesn't help

6 0

4 years ago

Read 2 more answers

Question 9 Multiple Choice Worth 1 points)

beks73 [17]