Log in
Mathematics
1
answer
0
watching
149
views

Show that a cubic function (a third-degree polynomial) always has exactly one point of inflection. If its graph has three x-intercepts x1, x2, and x3, show that the x-coordinate of the inflection point is.

Watch
1
answer
0
watching
149
views

For unlimited access to Homework Help, a Homework+ subscription is required.

Patrina Schowalter
Patrina SchowalterLv2
26 May 2020

Unlock all answers

Get 1 free homework help answer.
Already have an account? Log in
Share

Related questions

For what values of c does the polynomial have two inflection points? One inflection point? None? Illustrate by graphing P for several values of c. How does the graph change as c decreases?

Tynup Solution:

Given:

Differentiating

For c โ‰  0, there are two distinct roots for the equation.

Hence, for two inflection points the required condition is.

When c = 0, there is only one root for the equation.

Hence, when c = 0, the function has one inflection point.

Recall that the quadratic equation does not have real roots if its Discrimnant is less than zero.

Hence, for no inflection points

, which is not possible.

Hence, the polynomial function has minimum of one inflection point.

For different values of c

The common inflection point is (0, 0) and other inflection point is,

Hence,

On decreasing the value of c, the inflection point moves towards positive quadrant.

24 4(3-1) [7] 6. Let f(x) = 12 6- (In 3)2 + 10%(x+1)2 ( 9 + log(x+1)2(x + 1)2014 be a function defined on the interval (0,0). Show that the graph of f(x) on the interval (0,0) has an inflection point.

The graph of the derivative f โ€˜of a continuous function f is shown.

(a) On what intervals is f increasing? Decreasing?

(b) At what values of x does f have a local maximum? Local minimum?

(c) On what intervals is f concave upward? Concave downward?

(d) State the x-coordinate(s) of the point(s) of inflection

(e) Assuming that f (0) = 0, sketch a graph of f.

Weekly leaderboard

Home
Homework Help 3,900,000
Mathematics 240,000
Start filling in the gaps now
Log in