Question

For the function f(x) = x^6 − 15x^4

c) Will the graph have any standard symmetry? If so, which?

f) Determine the end-behavior (in both directions.)

g) Find the function's critical value(s), (if any.) Include their y-coordinates. (Exact values are expected, not decimals.)

h) Classify the critical points you just found by using the first derivative test.

i) Find the function's hyper-critical point(s), (if any.) Include their y-coordinates. (Exact values are expected, not decimals.)

j) Determine whether the points you just found are actual inflection points by making a chart of concavity changes for the function. List all points (both coordinates) that are actual inflection points as your answer. k) Make a complete graph of the function. Include on your graph all of the information you found above.

Answer 1

Solution f(W) = x 8 - 15x7 1 (c) The graph of f(a) is symmetric about the y-anis & have den functione so symmetric about y-aris. (B) The end behaviour means behavion as x x &x - - D. Here f(u) is even function and abdominant as a n approach infinity. The's means that as x - x The value of function also approaches. I infinity . 19 Critical values. f' (u) = 6x5 - 15 x 4 43 = 0 - 6x3(x² - 10) = 0 Critical x=0, x= + Jiol pants at these values the y-coordinates an y=0, y = -5oo. The Critical values are (0,0), (Sol, 500). (- Jool, 500)

1000 | 500 - - -500