how can you solve average rate of change in f(x)=4x^2+9 in following points?
A) (c,g) (r,u)
B) 2x+h
y(r) = 4 r^2 + 9 = u
y(c) = 4 c^2 + 9 = g
----------------------subtract
y(r)-y(c) = 4(r^2-c^2) = u-g =delta y
delta x = (r-c)
delta y/delta x
= 4(r^2-c^2)/(r-c)
= 4(r+c)
I do not understand B
B is (x+h) and f(x+h) which I believe equals 2x+h
Oh, I do not know what your belief means but I know what
x+h and f(x+h) means.
They are trying to lead you to calculus
f(x+h) = 4(x+h)^2 + 9
f(x) = 4 x^2 + 9
-----------------subtract
delta y =4[x^2 + 2 x h + h^2 -x^2]
= 4 (2 x h + h^2)
delta x = h
so
delta y/delta x = 4(2x + h)
END OF YOUR PROBLEM
Oh my look what we have here as h ---> 0 !!
delta y/delta x --> 4 (2x)
That is called the DERIVATIVE !!!
that is
That is important.
No I do not. I haven't taken calculus at all. I'm barely in college algebra.
To solve for the average rate of change of a function, you need to find the difference in the function values at two given points, and then divide that difference by the difference in the input values (also known as the interval between the points).
A) (c, g) (r, u)
To find the average rate of change between points (c, g) and (r, u) in the function f(x) = 4x^2 + 9, you can follow these steps:
1. Evaluate the function at each point using the given coordinates.
- Substitute c and g into the function: f(c) = 4c^2 + 9
- Substitute r and u into the function: f(r) = 4r^2 + 9
2. Calculate the difference in the function values:
- Subtract the function value at the first point (f(c)) from the function value at the second point (f(r)): f(r) - f(c)
3. Calculate the difference in the input values:
- Subtract the x-coordinate of the first point (r) from the x-coordinate of the second point (c): r - c
4. Finally, divide the difference in function values by the difference in input values to find the average rate of change:
- Average Rate of Change = (f(r) - f(c)) / (r - c)
B) 2x + h
To find the average rate of change of the function f(x) = 4x^2 + 9 when it is transformed by 2x + h, you need to define two points on the transformed function and then follow the steps mentioned above.
1. Choose two points on the transformed function, denoted by (x1, f(x1)) and (x2, f(x2)). The x-values can be any two real numbers.
2. Evaluate the transformed function at each point:
- Substitute x1 into the transformed function: (2x1 + h)
- Substitute x2 into the transformed function: (2x2 + h)
3. Calculate the difference in the transformed function values:
- Subtract the transformed function value at the first point [(2x1 + h)] from the function value at the second point [(2x2 + h)]: (2x2 + h) - (2x1 + h)
4. Calculate the difference in the input values:
- Subtract the x-coordinate of the first point (x2) from the x-coordinate of the second point (x1): x2 - x1
5. Finally, divide the difference in the transformed function values by the difference in input values to find the average rate of change:
- Average Rate of Change = [(2x2 + h) - (2x1 + h)] / (x2 - x1)
Note: The specific values of c, g, r, u, x1, x2, and h will determine the numerical answer to these problems.