Methods 3/4 questions

[zah]

PART 3
let p:r -> r where p(x) = x^3-6x^2-40x+192 and x1,x2,x3 are the x coordinates of the 3 distinct horizontal axis intercepts of p in order from left to right
a. Find the equation of the tangent to the graph of p at the midpoint of x1 and x2. Show that this tangent passes through the horizontal axis at x3. Draw a graph that illustrates this situation.
b. Show that a similar result holds for the tangent to the graph at p at the midpoint of x1 and x3 and also for the tangent to the graph of p at the midpoint of x2 and x3.
c. formulate the conjecture based on the results in a. and b. above and investigate whether this conjecture holds for any cubic polynomial function.
PART 4
a. show that the containing the oarts (x1+x2/2,q (x1+x2/2)) and (x3,0) has the same equation as the tangent to q at x1+x2/2. draw a graph to illustrate the situation
b. repeat part a for the other 2 combinations of midpoints and intercepts.
c. explain the relationship between this result and your conjecture from part 3.

[zah]

need hepl if anyone can help me

[brightsky]

So the points x1, x2, x3 are -6, 4, 8 respectively.

Midpoint of x1 and x2 is -1.





So the tangent is

When x = -1 on the cubic, y = -1 - 6 + 40 + 192 = 225.

So the line passes through point (-1, 225).

Substitute these points in:







So the equation is y = -25x + 200.

x3 is point (8,0).

If you substitute this in:



We have .

Hence the line does go through x3.

[zah]

thanxxxxxxx u soo sooo much

[zah]

what is PART 4