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choli [55]
3 years ago
6

Calculate the average rate of change of f(x) = x2 - 1 x - 4 for 2 ≤ x ≤ 6.

Mathematics
2 answers:
hoa [83]3 years ago
8 0

Answer:

Hence, the average rate of change is:

\dfrac{97}{12}

Step-by-step explanation:

We are asked to calculate the average value of the function:

f(x)=x^2-\dfrac{1}{x}-4 in 2 ≤ x ≤ 6

The average rate of change of the function f(x) in the interval 2 ≤ x ≤ 6  is given as:

\dfrac{f(6)-f(2)}{6-2}\\\\=\dfrac{f(6)-f(2)}{4}

Now,

f(6)=36-\dfrac{1}{6}-4\\\\f(6)=32-\dfrac{1}{6}\\\\f(6)=\dfrac{191}{6}

f(2)=4-\dfrac{1}{2}-4\\\\\\f(2)=-\dfrac{1}{2}

Hence, the average rate of change is:

\dfrac{\dfrac{191}{6}-\dfrac{-1}{2}}{4}\\\\=\dfrac{194}{6\times 4}\\\\=\dfrac{97}{12}

Hence, the average rate of change is:

\dfrac{97}{12}

rusak2 [61]3 years ago
5 0

Answer:

Step-by-step explanation:

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