The graph of function y =f(x)
is shown at the bottom.
a) Estimate the intervals where the function is increasing.
b) Estimate the intervals where f'(x) < 0
.
c) Estimate the coordinates of the critical points.
d) Estimate the equations of any vertical asymptotes.
e) . If x \geq -6
, estimate the intervals where f'(x) < 0
and f''(x) > 0
.
f) Identify a point of inflection, and state the approximate ordered pair for the point.
a) Determine the critical points of the function f(x) = 2x^4 -8x^3 - x^2 +6x
.
b) Classify each critical point in part a.
Sketch the graph of a function with the following properties:
x <1
.Check the function \displaystyle
g(x) = \frac{x^2 + 7x + 10}{(x -3)(x +2)}
for discontinuities. Conduct appropriate tests to determine if asymptotes exist at the discontinuity values. State the equations of any asymptotes and the domain of g(x).
Sketch ha graph of a function f with all of the following properties:
x < -2
and when $- 2< x < 4$`.x > 4
.f'(-2) =0, f'(4) = 0
x < -2
and when 3 < x < 9
.-2 < x < 3
and when x > 9
.Use at least five curve-sketching techniques to explain how to sketch the graph of the function \displaystyle
f(x) = \frac{2x + 10}{x^2 -9}
. Sketch the graph on graph paper.
The function f(x) = x^3 + bx^2 +c
has a critical point at (-2 , 6)
.
a) Find the constants b
and c
.
b) Sketch the graph of f(x)
using only the critical points and the second derivative test.