The function f is defined by f(x)=cos(3x). What is the average value of f' on the interval [-4, 0]? You may use a calculator and round your answer to the nearest thousandth. ^DELTA MATH^

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis:

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus

i'm pretty sure the answer is a. decreases with increase in