Let f(x)= cos(2x) +e^(-x). for what value of x on the interval (0,3) will f have the same instantaneous rate of change as the average rate of change of f over the interval?

is continuous on [0, 3] and differentiable on (0, 3), so the mean value theorem applies here. It says that there is some in the open interval (0, 3) such that

We have

so

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

answer:

1.14285714286

step-by-step explanation:

divide 40 into 35 and you will get your answer