Question

Find the average rate of change of f ( x ) = -2x^2 + 4x + 2 as X varies from 1.2 to 3.8

Answer 1

Here we need to find the average rate of change of $f(x)$.

Now,

$f(x)=-2x^2+4x+2$

Let us find out the value of $f(x)$ at the point $x=1.2$.

Plugging $x=1.2$ in the equation we get:

$f(1.2)=-2(1.2)^2+4(1.2)+2=-2\times 1.44+4.8+2=-2.88+4.8+2=3.92$

So,

$f(1.2)=3.92$

Now calculating the value of $f(x)$ at $x=3.8$.

$f(3.8)=-2(3.8)^2+4(3.8)+2=-2(14.44)+15.2+2=-28.88+15.2+2=-11.68$

So,

$f(3.8)=-11.68$

Now that we have the values of the function at two distinct points, we can find the average by using the formula given below:

$Avg= \frac{sum}{n}$, where 'n' represents the number of values and that is two in our case and sum represents the sum of the values of the function.

Therefore,

$Avg= \frac{3.92+(-11.68)}{2} =\frac{-7.76}{2} =-3.88$

So, the average rate of change of the function $f(x)$ from 1.2 to 3.8 is $-3.88$.