f(x)=5x^4-45x^2 a. roots and multiplicities b. tendancies/end behaviors c. number of curves d. y-intercept e. sketch the graph

Answer 1

0 is one root with multiplicity 2. you can factor out x^2 = (x-0)(x-0)

that leaves 5x^2-45 which factors into 5(x^2-9) = 5(x-3)(x+3)

roots are 0,0,3, and -3

y intercept is 0. f(0) = 0. that's (0,0) the origin

the graph is "W" shaped, with the local max = 0, no global maximum, when x approaches negative or positive infinity, f(x) approaches positive infinity

local minimums are at x=-3/sqr2 and x= 3/sqr2, both have y values that are negative