What is the average rate of change for the function f(x)=x^2+4 for the domain of -2 to 4

Mathematics

1 answer:

Neko [114]2 years ago

5 0

Answer:

Step-by-step explanation:

For a quadratic function the average rate of change on an interval is the rate of change at the midpoint of the interval. The rate of change of a function is given by its derivative.

The derivative of f(x) = x^2 is f'(x) = 2x. The midpoint of the interval is (4+(-2))/2 = 1. Then the average rate of change is ...

f'(1) = 2(1) = 2

The average rate of change of f(x) on [-2, 4] is 2.

<em>Alternate solution</em>

The average rate of change is the slope of the line between the end points of the interval:

m = (y2 -y1)/(x2 -x1)

m = (f(4) -f(-2))/(4 -(-2)) = (20 -8)/(6) = 2

The average rate of change on [-2, 4] is 2.

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The attached graph shows the points on the curve and a line with slope 2 between them. It also shows the various slope calculations.

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Plz help me with this plz

const2013 [10]

Answer:

Slope: $-\frac{3}{4}$

Y intercept: 7

Equation: $y=-\frac{3}{4}x+7$

Step-by-step explanation:

The slope is found by doing the equation $\frac{rise}{run}$ . When looking at the first two points, it's shown that the rise (difference between the two y values) is -3 (since it decreased by 3) and the run (difference between the two x values) is 4 (since it increased by 4).