Given the two points (0,4) and (2, 6), what would the numerator of the equation for slope be?

Using function concepts, it is found that the correct options are:

• A. The functions are approximately equal on the interval 1.9 smaller than or equal to x larger than or equal to 2.1.
• E. The graphs intersect at the point (2,1).
• F. The slope of the line equals g'(2).

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• The value of x we are interested is x = 2, thus, considering a margin, the functions are approximately equal between x = 1.9 and x = 2.1, which means that option A is correct, while option D is not.
• The y-interceptof g is , while the y-intercept of L is . Not the same, thus, option B is not correct.
• The slope of the tangent line to g at x = 2 is the derivative of g at x = 2, that is, g'(2), thus option F is correct while option C is not.
• At (2,1), the g(x) and L(x) intersect, thus, option E is correct.

A similar problem is given at brainly.com/question/22426360

well, about A and D, I just plugged the values on the slope formula of

for A the values are 8.01 and 8.0, so indeed those "slopes" are close.

for D the values are -2.25 and 8.0, so no dice on that one.

for B, let's check the y-intercept for g(x), by setting x = 0, we end up g(0) = 0³-4(0)+1, which gives us g(0) = 1.

checking L(x) y-intercept, well, L(x) is in slope-intercept form, thus the +1 sticking out on the far right is the y-intercept, so, dice.

for C, well, the slope if L(x) is 8, since it's in slope-intercept form, the derivative of g(x) is g'(x) = 3x² - 4, and thus g'(0) = -4, so no dice.

for E, do they intercept at (2,1)?  well, come on now, L(x) is a tangent line to g(x), so that's a must for a tangent.

for F, we know the slope of the line L(x) is 8, is g'(2) = 8?  let's check

recall that g'(x) = 3x² - 4, so g'(2) = 3(2)² - 4, meaning g'(2) = 8, so, dice.