Question

The expression below can be thought of as the slope of a secant line between 2 points on the graph of a function. Please indicate i) What the two points are ii) What the function is

((x-b)^4-x^4)/b

Answer 1

this drawing graph illustrates the principal of the problem with slope, original graph, secant line

Answer 2

I am confused as to how the question gets (x-b) rather than x+b.

Answer 3

the function in this case looks different (look picture) but the mechanism is the same

@Melody123 haha, I didn't even notice that!!

Answer 4

I guess, based on the definition given above, the points would be (x,f(x)) and (x-b, f(x-b)). Then the equation could just be written as ((x^4)-(x-b)^4)/(x-(x-b)) which is equivalent.

Answer 5

@Melody123 the equation you give is of the secant line. I believe they want the equation from the original function, that the secant line cuts

Answer 6

if you compare two points, and divide them by some number, it's a line :)

so the equation ((x^4)-(x-b)^4)/(x-(x-b)) is a line, since the x-terms are actually just points

Answer 7

You can look at it from the beginning:

if they had used f(x) = x^4, then the secant line for this function would be:

from x, to x-b:
(x-b)^4 - (x)^4 / x-b-x

^this one is exactly what the problem gives us for secant line.

Answer 8

But this is (x-b)^4-x^4/-b, which is not our answer. I have been struggling for a while, I'm not sure if there is a typo, or if this is possible?