Question

Help Please!!!!!!! Water coming out from a fountain is modeled by the function f(x) = -x2 + 7x + 5 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds.

What does the average rate of change of f(x) from x = 4 to x = 6 represent?

The water falls down with an average speed of 5 feet per second from 4 seconds to 6 seconds.

The water falls down with an average speed of 3 feet per second from 4 seconds to 6 seconds.

The water travels an average distance of 5 feet from 4 seconds to 6 seconds.

The water travels an average dista

Answer 1

Do you guys need answer D to be shown the last answer??

Answer 2

@vishweshshrimali5 Here is my first question

Answer 3

See, since you have to obtain rate of change of f(x), so, calculate f'(x) i.e. the first derivative of f(x) w.r.t. x.

Answer 4

@vishweshshrimali5 You mean with the x=4 and x=6

Answer 5

So can you tell me the value of f(x).

Answer 6

Then tell the value of f'(x).

Answer 7

so do 4 times 6 @vishweshshrimali5

Answer 8

No no. First calculate f'(x). Then find out f'(4) and f'(6) and take their mean or average value.

Answer 9

tthe f(x) is -x^2 @vishweshshrimali5

Answer 10

No f(x) is \(-x^2 + 7x + 5\)

Answer 11

Average value of rate of change of f(x) will be
\[\cfrac{f'(6) - f'(4)}{6-4}\]

Answer 12

okay i got it 6-4=2 7x+5=12 @vishweshshrimali5