contestada

Find the value of constant k (or indicate that no such value of k exists), so that the average rate of change in F(t) = kt^2 on the interval [-1, 2] is equal to 1. K = ________

Respuesta :

Answer:

k = 1

Explanation:

Given the function:

[tex]f(t)=kt^2[/tex]

The average rate of change is given by the formula:

[tex]R=\frac{f(b)-f(a)}{b-a}[/tex]

where a = -1, b = 2

[tex]\begin{gathered} R=\frac{2^2k-(-1)^2k}{2-(-1)} \\ \\ =\frac{4k-k}{2+1} \\ \\ =\frac{3k}{3}=k \end{gathered}[/tex]

Now, the rate of change has been given to be 1, so

[tex]R=k=1[/tex]

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