Answer: sorry don’t know
Step-by-step explanation:
The picture is not showing up :(
That is basically the slope
that would be
or
both will yeild the averge rate of change
Hi there!
A.) Begin by verifying that both endpoints have the same y-value:
g(-1) = 2(-1)² - 4(-1) + 3
Simplify:
g(-1) = 2 + 4 + 3 = 9
g(2) = 2(2)² - 4(2) + 3 = 8 - 8 + 3 = 3
Since the endpoints are not the same, Rolle's theorem does NOT apply.
B.)
Begin by ensuring that the function is continuous.
The function is a polynomial, so it satisfies the conditions of the function being BOTH continuous and differentiable on the given interval (All x-values do as well in this instance). We can proceed to find the values that satisfy the MVT:
Begin by finding the average rate of change over the interval:
Now, Find the derivative of the function:
g(x) = 2x² - 4x + 3
Apply power rule:
g'(x) = 4x - 4
Find the x value in which the derivative equals the AROC:
4x - 4 = -2
Add 4 to both sides:
4x = 2
Divide both sides by 4:
x = 1/2
Slope Intercept Form Equation: mx + b = y
Use the slope, like 3/2 or 4, but first plot the y-intercept, like 3, and then put the equation to these: y = 3/2x + 4 or y = 4x + 4. Plot the y-intercept on the y- axis (the vertical line). If you were to use my examples, you would plot the y-intercept by (0,4). Then if you used my first example equation, move 2 to the right of the plotted coordinates and then up by 3. If you were to use my second equation, however, then you would move to the left of the same plotted coordinates, (0,4), 1 to the right and then up 4.