What is the average rate of change for ƒ(x) = −2x + 70 over the interval 2 ≤ x ≤ 6?
1 answer:
Answer:
The average rate of change is -2
Step-by-step explanation:
we know that
To find out the average rate of change, we divide the change in the output value by the change in the input value.
In a linear function the average rate of change is a constant and is equal to the slope of the function
The linear function in slope intercept form is equal to
where
m is the slope or unit rate of the linear function
b is the y-intercept or initial value of the linear function
In this problem we have
so
therefore
The average rate of change is -2
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Answer:
x = 2 cm
y = 2 cm
A(max) = 4 cm²
Step-by-step explanation: See Annex
The right isosceles triangle has two 45° angles and the right angle.
tan 45° = 1 = x / 4 - y or x = 4 - y y = 4 - x
A(r) = x* y
Area of the rectangle as a function of x
A(x) = x * ( 4 - x ) A(x) = 4*x - x²
Tacking derivatives on both sides of the equation:
A´(x) = 4 - 2*x A´(x) = 0 4 - 2*x = 0
2*x = 4
x = 2 cm
And y = 4 - 2 = 2 cm
The rectangle of maximum area result to be a square of side 2 cm
A(max) = 2*2 = 4 cm²
To find out if A(x) has a maximum in the point x = 2
We get the second derivative
A´´(x) = -2 A´´(x) < 0 then A(x) has a maximum at x = 2
