Suppose f is defined by f(x)=3x/(4+x^2), −1≤x<3. What is the domain of f? Find the intervals...

Suppose f is defined by f(x)=3x/(4+x^2), −1≤x<3.

What is the domain of f?

Find the intervals where f is positive and where f is negative.

Does f have any horizontal or vertical asymptotes. If so, find them, and show your supporting calculations. If not, briefly explain why not.

Compute f′ and use it to determine the intervals where f is increasing and the intervals where f is decreasing.

Find the coordinates of the local extrema of f

Make a rough sketch of the graph of f using only the information from the previous steps.

Expert Solution

milcah answered 2 years ago

Find intervals of increase/decrease, max/min values, intervals of concavitiy. f(x)=x^3 -3x^2 +2

How do you find the domain of: f(g)= 5x^2+4 f(g)= 3x; -2<x<6 f(g)= (1) / 3x-6...

How do you find the domain of: f(g)= 5x^2+4 f(g)= 3x; -2<x<6 f(g)= (1) / 3x-6 f(g)= (x+2) / x^2-1 f(g)= x^4 / x^2+x-6 f(g)= sqrt (x+1) f(g)= sqrt (x^2+9)

(a) For f(x) = 1 4 x 4 − 6x 2 find the intervals where f(x)...

(a) For f(x) = 1 4 x 4 − 6x 2 find the intervals where f(x) is concave up, and the intervals where f(x) is concave down, and the inflection points of f(x) by the following steps: i. Compute f 0 (x) and f 00(x). ii. Show that f 00(x) is equal to 0 only at x = −2 and x = 2. iii. Observe that f 00(x) is a continuous since it is a polynomial. Conclude that f 00(x)...

part 1) Let f(x) = x^4 − 2x^2 + 3. Find the intervals of concavity of...

part 1) Let f(x) = x^4 − 2x^2 + 3. Find the intervals of concavity of f and determine its inflection point(s). part 2) Find the absolute extrema of f(x) = x^4 + 4x^3 − 8x^2 + 3 on [−1, 2].

f(x)= 9x^4-2x^3-36x^2+8x/3x^3+x^2-14 -Factor the numerator and denominator of f(x) completely. -Write the domain of f(x) in...

f(x)= 9x^4-2x^3-36x^2+8x/3x^3+x^2-14 -Factor the numerator and denominator of f(x) completely. -Write the domain of f(x) in interval notation. -Locate all hole(s), if any, and write them in the form of coordinate pairs. -Locate all vertical asymptote(s), if any, and give their equations in the form x = c. For each one, describe what happens to f(x) as x approaches c from the left(-), and as x approaches c from the right (+). -Locate the horizontal/slant asymptote, if any, and give...

The function f(x)=3x+2 is one-to-one a) find the inverse of f b) State the domain and...

The function f(x)=3x+2 is one-to-one a) find the inverse of f b) State the domain and range of f c) State the domain and range of f-1 d) Graph f,f-1, and y=x on the same set of axes

A. In the following parts, consider the function f(x) =1/3x^3+3/2x^2−4x+ 7 (a)Find the intervals on which...

A. In the following parts, consider the function f(x) =1/3x^3+3/2x^2−4x+ 7 (a)Find the intervals on which f is increasing/decreasing and identify any local extrema. (b) Find the intervals on which f is concave up/down and find any inflection points. B. Consider the function f(x) = sin(x) + cos(x). Find the absolute minimum and absolute maximum on the interval [−π,π].

Question

Suppose f is defined by f(x)=3x/(4+x^2), −1≤x<3. What is the domain of f? Find the intervals...

Solutions

Expert Solution

Related Solutions