Find the average rate of change of y with respect to x for the function:?

Question

y= -5x^2-x+12 for the interval from x= -2 to x=1

answer given is 4

Answer 1

y(-2) = -5*(-2)² - (-2) + 12
= -20 + 2 + 12
= -6

y(1) = -5*1² - 1 + 12
= 6

Average rate of change = [y(1) - y(-2)] / [1 - (-2)]
= (6+6) / (1+2)
= 12/3
= 4

Answer 2

To get the average rate, you have to integrate the rate on the interval [21, 1] then divide by the length of the interval (which is 3).

In order to get the rate of change, you need to take the derivative of y with respect to x (dy/dx). Integrating this, you need the antiderivative -- which is just y.

Therefore -- the answer is (y(1)-(y(-2))/3

Work this out -- and you get 4

Answer 3

With x = 2, we get y = (2 + a million)/2 or y = 3/2. in this situation, touching on the factor of the function: (2, 3/2). With x = 3, we get y = (3 + a million)/3 or y = 4/3. in this situation, touching on the factor of the function: (3, 4/3). Connecting the two factors will style a "secant line" to the function. the fundamental fee of substitute refers back to the "slope" of this line. the logo for it is ?y/?x (study as "substitute in y over substitute in x" or basically the slope), and we evaluate through basically applying the slope formulation: ?y/?x = (y2 - y1)/(x2 - x1) consequently, the fundamental fee of substitute of the function y = (x + a million)/x from x = 2 to x = 3 is: ?y/?x = (4/3 - 3/2)/(3 - 2) ?y/?x = (8/6 - 9/6)/a million ?y/?x = -a million/6 desire this helps^_^

Answer 4

The average rate of change of a function on [a,b] is the slope of the secant line connecting (a,f(a)) and (b,f(b)).

avg rate of change = [f(a)-f(b)]/(a-b)

m = ([-5(-2)^2-(-2)+12]-[-5(1)^2-(1)+12])/(-2-1)

m = ([-20+2+12]-[-5-1+12])/-3

m = (-6-6)/-3

m = -12/-3

m = 4