# increasing decreasing and more

How to analytically find the intervals on which the function y = 2x^4 - 4x^2 + 1 is
1)increasing
2)decreasing
3)concave up
4)concave down

Also find any local extreme values and inflection points.

Thanks.

(1) The function is increasing when the first derivative dy/dx = 8x^3 - 8x is positive
(2) The function is decreasing there the same derivative is negative.
(3) The function is concave up where the second derivative, 24 x^2 - 8, is positive.
(4) The function is concave down where the second derivative is negative.
Extreme values occur whereever dy/dx = 0
Inflection points are where the second deritivative is zero.

The rest is algebra.

1. 👍 0
2. 👎 0
3. 👁 219

## Similar Questions

1. ### calculus 1

f(x) = 3x^3 - 9x + 5 find the: 1) zeroes or undefined values 2) intervals where the function is greater than zero 3) intervals where the function is less than zero 4) coordinates of all maxima and minima 5) intervals where the

asked by i on March 3, 2016
2. ### math

. Given the following function, f(x)=-x^2 -8x find: (a) vertex, (b) axis of symmetry, (c) intercepts, (d) domain, (e) range, (f) intervals where the function is increasing, (g) intervals where the function is decreasing, and (h)

asked by mz tee on November 10, 2011
3. ### math-calc

for x (-12, 10) the function f is defined: f(x)=x^7(x+2)^2 On which two intervals is the function increasing (enter intervals in ascending order)? Find the region in which the function is positive Where does the function achieve

asked by mkcolema on March 13, 2009
4. ### algebra

Given the following function, find: (a) vertex (b) axis of symmetry (c) intercepts, (d) domain (e) range (f) intervals where the function is increasing, (g) intervals where the function is decreasing Please show all of your work

asked by sarah on January 18, 2012
5. ### Maths

Question – 1: The gradient of the graph of f(x) at any point is,ax^2-12x + 9, and the point,(2,-3),is an inflection point of f(x). (a) Find the value of the real constant, a. Find the function f(x). (b) Find the stationary

asked by Victoria on May 10, 2008
6. ### math-calc

Consider the function f(x)= (2x+8)/(6x+3). For this function there are two important intervals: (-inf, A) (A, inf) and where the function is not defined at A . Find A For each of the following intervals, tell whether is increasing

asked by mkcolema on March 13, 2009
7. ### Math

For x [–14,13] the function f is defined by f(x)=(x^3)(x+6)^4 On which two intervals is the function increasing (enter intervals in ascending order)? I got increasing intervals between [-14, -6], but can't find the other

asked by Jay111 on November 24, 2008
8. ### Calculus

Consider the function f(x)=ln(x)/x^6. For this function there are two important intervals: (A,B] and [B,∞) where A and B are critical numbers or numbers where the function is undefined. Find A Find B For each of the following

asked by Hailey on October 20, 2014
9. ### calc

Consider the function below. (Round the answers to three decimal places. If you need to use - or , enter -INFINITY or INFINITY.) f(x) = 4 + 4x2 - x4 (a) Find the intervals of increase. (Enter the interval that contains smaller

asked by Anonymous on April 3, 2010
10. ### Calc

f(x) = x^2 / (x - 7)^2 (a) Find the vertical and horizontal asymptotes. x= y= (b) Find the interval where the function is increasing. Find the intervals where the function is decreasing. (Enter the interval that contains smaller

asked by Bobby on November 16, 2009

More Similar Questions