Find the average rate of change of the function f(x)=(3/-3x-5), on the interval x ∈ [0,3]

Mathematics

1 answer:

Svet_ta [14]2 years ago

4 0

Answer:

The average rate of change on the given interval is 9/70

Step-by-step explanation:

Here, we are to find the average rate of change of the function on the given interval

We proceed as follows;

on an interval [a,b] , we can find the average rate of change using the formula;

f(b) - f(a)/b-a

From the question;

a = 0

b = 3

f(0) = -3/5

f(3) = -3/14

Substituting the values, we have;

-3/14-(-3/5)/3-0

= 3/5-3/14/3

= (42-15)/70/3

= 27/70/3

= 27/70 * 1/3 = 9/70

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$4x^2+4x+xy=5\implies 8x+4+\stackrel{\textit{product rule}}{\left( 1\cdot y+x\cdot \cfrac{dy}{dx} \right)}=0 \\\\\\ x\cfrac{dy}{dx}=-8x-4-y\implies \cfrac{dy}{dx}=\cfrac{-8x-4-y}{x}$

now, we know that y(5) = -23, which is another way of saying that when x = 5, y = -23, but we already knew that, we can get that by simply plugging it into the equation hmmm y'(5), well

$\left. \cfrac{dy}{dx}=\cfrac{-8x-4-y}{x} \right|_{\stackrel{x=5~}{\textit{\tiny y=-23}}}\implies \cfrac{-8(5)-4-(-23)}{5}\implies \cfrac{-21}{5}$