Question

G(x)= -\dfrac{x^2}{4} + 7g(x)=− 4 x 2 ​ +7g, left parenthesis, x, right parenthesis, equals, minus, start fraction, x, squared, divided by, 4, end fraction, plus, 7 What is the average rate of change of ggg over the interval [-2,4][−2,4]open bracket, minus, 2, comma, 4, close bracket?

Answer 1

-1/2

Explanation:

Given the function
`G(x)= -(x^2)/(4) + 7`, the average rate of change of g(x) over the interval [-2,4], is expressed as shown below;

Rate of change of the function is expressed as g(b)-g(a)/b-a

where a - -2 and b = 4

`G(4)= -(4^2)/(4) + 7\\G(4)= -(16)/(4) + 7\\G(4)= -4 + 7\\G(4) = 3\\`

`G(-2) = -((-2)^2)/(4) + 7\\G(-2)= -(4)/(4) + 7\\G(-2)= -1 + 7\\G(-2)= 6`

average rate of change of g(x) over the interval [-2,4] will be;

`g'(x) = (g(4)-g(-2))/(4-(-2))\\ g'(x) = (3-6)/(6)\\\\g'(x) = -3/6\\g'(x) = -1/2`