Question

G(x)=− 4 x 2 ​ +7g, left parenthesis, x, right parenthesis, equals, minus, start fraction, x, start superscript, 2, end superscript, 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

For this case, what we should do is evaluate the function for different points within the range shown.
 We then have the following table:
 x      g(x) 
 -2    -9
 -1     3
  0     7
  1     3
  2    -9
  3    -29
  4    -57
 From where we observed that the average rate of change is:
 -13
 Answer:
 the average rate of change of g over the interval [-2,4] is:
 -13

Answer 2

The average rate of change of g over the interval [-2,4] for the given function G(x)=− 4 x 2 ​ +7g is -1/2.

What is the average rate of change?

The average rate of change of a function is the change in the value of one variable or quantity in a fixed time interval.

The average rate of change of the is the ratio of change in y values to the change in x values of the data.

$r=\dfrac{g(b)-g(a)}{b-a}$

Here, a and b are the variable.

The given function in the problem is,

$G(x)=-\dfrac{x^2}{4} +7$

For the interval [-2,4], the function gives the value as,

$g(-2)=-\dfrac{(-2)^2}{4} +7\\g(-2)=-\dfrac{4}{4} +7\\g(-2)=6$

For value 4,

$g(4)=-\dfrac{(4)^2}{4} +7\\g(4)=-\dfrac{16}{4} +7\\g(4)=3$

Average rate of change is,

$r=\dfrac{g(4)-g(-2)}{4-(-2)}\\r=\dfrac{3-6}{6}\\r=-\dfrac{1}{2}$

Thus, the average rate of change of g over the interval [-2,4] for the given function G(x)=− 4 x 2 ​ +7g is -1/2.

Learn more about the rate of change here;

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