Let h be the function with derivative given by h′(x)=4e^{cosx} . At what value of x in the interval −3 ≤ x ≤ 0 does the instantaneous rate of change of h equal the average rate of change of f over the interval −3 ≤ x ≤ 0?

36 is the final answer! : )

so, converting firstly the mixed fractions to improper fractions and then "adding".

since we know that the two functions are equal, f (x) = g

(x), therefore when we equate the two equations the result should be similar to

3x = x – 4:

a. f(x) = 3x, g(x) = x – 4

equating the two functions:

3x = x – 4             (correct)

so we now got our answer (a)

the translated point is (5,2)