Respuesta :
A reasonable estimate of the rate of change for the interval
300 ≤ x ≤ 400 considering if the company is making a profit=2.
Consider the Quadratic relationship, between the selling price for its newest tablet and the company's daily profit is given,
f(x)= a x² + b x + c
Differentiating once
f'(x)= 2 a x + b
As we have to find the rate of change for the interval 200 ≤ x ≤ 300.
So,[tex]f(300)= 2 a \times 300 + b= 600a+b[/tex]
[tex]f(400)= 2 a \times 400 + b= 800 a + b[/tex]
Rate of change for the interval 300 ≤ x ≤ 400
What is the formula for the rate of change?
[tex]=\frac{f(b)-f(a)}{b-a}[/tex]
[tex]=\frac{800 a + b-(600 a + b)}{400-300} \\=\frac{800 a + b-600 a -b)}{100}\\\\=\frac{(200 a )}{100}\\\\=2a[/tex]
As considering, if the company is going through Profit, when the selling of the tablet is in the interval (300 ≤ x ≤ 400),
So, a Reasonable estimate of the rate of change for the interval 300 ≤ x ≤ 400 considering if the company is making a profit=2
Option (A).
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