The rate of change of the given function at [-1,3] is 5
Further explanation:
Given function is:
[tex]f(x) = 4x^2-3x-4[/tex]
And the interval is:
[-1,3]
In order to find the rate of chnage of function the given function's value is calculated at both points and divided by their difference
The formula is:
[tex]Rate\ of\ change= \frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
Here,
x_1 = -1
x_2 = 3
So,
[tex]f(-1) = 4(-1)^2-3(-1)-4\\=4(1) +3-4\\=4-1\\=3\\f(3) = 4(3)^2-3(3)-4\\= 4(9)-9-4\\=36-13\\=23[/tex]
Putting the values in the rate of change formula:
[tex]Rate\ of\ change= \frac{23-3}{3-(-1)}\\= \frac{23-3}{3+1}\\=\frac{20}{4} \\=5[/tex]
The rate of change of the given function at [-1,3] is 5
Keywords: Rate of change, functions
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