What is the average rate of change of the function fx= 2x2+ 3 over the interval [1,4]?

  10

Step-by-step explanation:

The average rate of change of f(x) on the interval [a, b] is found by ...

  m = (f(b) -f(a))/(b -a)

For your function, we have [a, b] = [1, 4}, so the rate of change is calculated as ...

  f(1) = 2·1² +3 = 5

  f(4) = 2·4² +3 = 35

  m = (35 -5)/(4 -1) = 30/3 = 10

The average rate of change on the interval is 10.

Comment on quadratic slope

The slope of a quadratic curve changes continuously in linear fashion. The average slope on any interval is the slope at the midpoint of the interval. Using derivatives, we find the slope of the quadratic ax^2+bx+c to be given by 2ax+b. For the function given here, that is 4x. The midpoint of [1, 4] is x=2.5, so the slope at the midpoint is 4(2.5) = 10, as above.

the answer is 200

step-by-step explanation:

the way the question is worded, it seems to imply the $264 interest is simple interest, not compound interest.

the simple interest for 2 years is $264; the simple interest for 1 year is $132.

$132 interest on a $600 investment means an interest rate of (132/600)*100 = 22%.

the value of $200 at 22% interest compounded annually for three years is

200%281.22%29%5e3

the amount of interest is that value, minus the original $200.

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol