Show that the inequality x^4 < 8x^2 + 9 is satisfied for when -3 < x < 3 .
(x^2 - 9)(x^2 + 1) < 0 solving the equation to get solutions to the equality (x^2 - 9)(x^2 + 1) = 0 : x = +/- 3 or x = +/- 1 now consider points either side of these x-intercepts... for x>3: equality is not satisfied for 1<x<3: equality is satisfied for -1<x<1: equality is satisfied for -3<x<-1: equality is satisfied for x<-3: equality is not satisfied
HT
Related MAT University answers
All answers ▸Let f(x) = 2x^3 − kx^2 + 2x − k. For what values of the real number k does the graph y = f(x) have two distinct real stationary points? (MAT 2017 q1.A)
We define the digit sum of a non-negative integer to be the sum of its digits. For example, the digit sum of 123 is 1 + 2 + 3 = 6. Let n be a positive integer with n < 10. How many positive integers less than 1000 have digit sum equal to n?
How many 0's are at the end of 100! (100 factorial)?
The sequence xn is given by the formula x_n = n^3 − 9n^2 + 631. What is the largest value of n for which x_n > x_(n+1)?