Question

f(x)=x^3+x^2-x-1 Follow each step to graph the function. a.) Find the x-intercepts. If there are none, state the fact. b) Find the y-intercepts. IF there are none, state the fact. c) Find any vertical asymptotes. If there are none, state the fact. d) Find any horizontal asymptotes. If there are none, state the fact. e) Find any slant asymptotes. If there are none, state the fact. f) Find f'(x) g) Find f"(x) h) Find the domain of f. i) Find the critical values of f. j) Use the Second-Derivative Test to find relative extrema. k) Find intervals where f is increasing or decreasing. Need to describe two intervals separately. l) Use the second derivative to determine the inflection points. m) Find the intervals where f is concave up or concave down. n) Sketch the graph of f. A rough sketch is fine, just make sure to label intercepts and asymptotes.

Answer 1

The x intercepts are the points at which y = 0

We have x = -1 and 1 where y is zero

Similarly y intercepts are the points at which x is zero

F(0) = -1

From the graph we don't have any asymptotes

f'(x) = 3x^2 + 2x - 1

f''(x) = 6x + 2

Domain of f(x) is R set of all real values for x

Critical values are the points at which first derivative is zero

X = -1 and x = 1/3

Inflection points are where the second derivative is zero

The inflection points are x = -3

The intervals in which f is increasing or decreasing can be find out from graph

The function is increasing from (- infinite ,-1) & [0.4,infinite)

The function is decreasing from (-1,0.4)