Hakim was feeling adventurous at lunch. Rather than choosing a single drink, he decided to

What is the average rate of change of f(x) = -x2 + 3x + 6 over the interval –3

Rufina [12.5K]

Answer:

$\frac{\Delta y}{\Delta x} =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3$

Step-by-step explanation:

To find the average rate of change of a function over a given interval, basically you need to find the slope. The mathematical definition of the slope is very similar to the one we use every day. In mathematics, the slope is the relationship between the vertical and horizontal changes between two points on a surface or a line. In this sense, the slope can be found using the following expression:

$Average\hspace{3}rate\hspace{3}of\hspace{3}change=Slope=\frac{y_2-y_1}{x_2-x_1} =\frac{f(x_2)-f(x_1)}{x_2-x_1}$

So, the average rate of change of:

$f(x)=-x^2+3x+6$

Over the interval $-3$

Is:

$f(x_2)=f(3)=-(3)^2+3(3)+6=-9+9+6=6\\\\f(x_1)=f(-3)=-(-3)^2+3(-3)+6=-9-9+6=-12$

$\frac{\Delta y}{\Delta x} =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3$

Therefore, the average rate of change of this function over that interval is 3.

3 0

2 years ago

Solve for x. 2=4x-6

77julia77 [94]

Answer:

x = 2

Step-by-step explanation:

Rewrite the equation as 4x - 6 = 2

Move all terms not containing x to the right side of the equation:

Add 6 to both sides of the equation.

4x = 2 + 6

Add 2 and 6.

4x = 8

Divide each term by 4 and simplify.

Divide each term in 4x = 8 by 4.

$\frac{4x}{4} =\frac{8}{4}$

Reduce the expression by cancelling the common factors.

$x=\frac{8}{4}$

Divide 8 by 4.

x = 2

8 0

2 years ago

Which expression is equivilent to 6(3x-4)+2x

motikmotik

Answer:

44x,

Step-by-step explanation:

you can expand the brackets which equals 18x + 24 (or subtract 24 if the expression is 6(3x-4)) at the end of the equation you will add 2 which would give you 44x

4 0

2 years ago

In a recent year, a hospital had 4588 births. Find the mean number of births per day, then use that result and the Poisson distr

Harman [31]

Answer:

4221 birhs

Step-by-step explanation:

. Find the mean number of births per day, then use that result to find the probability that in a day, there are 15 births.

4 0

2 years ago

Use the drop down menus to describe the relationship between the number of teaspoons and number of tablespoon

Keith_Richards [23]