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3 years ago

Given the function h(x)=-x^2-5x+14 determine the average rate of change of the function over the interval -9

Mathematics

1 answer:

Juli2301 [7.4K]3 years ago

8 0

Answer:

The average rate of change of the function over the interval is of 6.

Step-by-step explanation:

Average rate of change:

The average rate of change of a function h(x) over an interval [a,b] is given by:

$A = \frac{h(b)-h(a)}{b-a}$

In this question:

Over the interval [-9,-2], so $a = -9, b = -2, b - a = -2 -(-9) = 7$

The function is:

$h(x) = -x^2 - 5x + 14$

$h(-9) = -9^2 -5(-9) + 14 = -81 + 45 + 14 = -22$

$h(-2) = -2^2 -5(-2) + 14 = -4 + 10 + 14 = 20$

Then

$A = \frac{h(-2)-h(-9)}{7} = \frac{20-(-22)}{7} = \frac{42}{7} = 6$

The average rate of change of the function over the interval is of 6.

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bezimeni [28]

Step-by-step explanation:

Remember that in a linear function of the form $f(x)=mx+b$ , $m$ is the slope and $b$ is the why intercept.

Part A. Since $g(x)=2x+6$ , its slope is 2 and its y-intercept is 6

Now, to find the slope of $f(x)$ we are using the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

where

$m$ is the slope

$(x_1,y_1)$ are the coordinates of the first point

$(x_2,y_2)$ are the coordinates of the second point

From the table the first point is (-1, -12) and the second point is (0, -6)

Replacing values:

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{-6--(12)}{0-(-1)}$

$m=\frac{-6+12}{0+1}$

$m=6$

The slope of f(x) is bigger than the slope of g(x), which means the line represented by f(x) is stepper than the line represented by g(x).

Part B. To find the y-intercept of f(x) we are taking advantage of the fact that the y-intercept of a linear function occurs when x = 0, so we just need to look in the table for the value of f(x) when x = 0. From the table $f(x)=-6$ when $x=0$ ; therefore the y-intercept of $f(x)$ is -6.