# Calculus

posted by .

Consider the function f(x)=xlnx.

For the following questions, write inf for ∞, -inf for −∞, and None if no such answer exists.

a.) The domain of this function is .

b.) The x-intercept is .

c.) f′(x) = .

d.) f(x) is increasing on the interval and decreasing on .

e.) f(x) has a local minimum at and a local maximum at .

f.) f′′(x) = .

g.) f(x) is concave up on the interval and concave down on .

h.) f(x) has a point of inflection at .

## Similar Questions

A continuous function f, defined for all x, has the following properties: 1. f is increasing 2. f is concave down 3. f(13)=3 4. f'(13)=1/4 Sketch a possible graph for f, and use it to answer the following questions about f. A. For …
2. ### Calculus

Consider the function f(x)=x−15x^1/3. For the following questions, write inf for ∞, -inf for −∞, U for the union symbol, None if no answer exists, and separate by a comma if more than one answer exist. a.) The …
3. ### Calculus

Consider the function f(x)=3cosx−cos^(3)x for 0<x<2π. For the following questions, write inf for ∞, -inf for −∞, U for the union symbol, None if no answer exists, and separate by a comma if more than …
4. ### Math

Can someone help me with these T.T 1.Which polynomial function would have the end behaviour of as x-> -∞, y= +inf and as x-> ∞, y-> -∞?

The domain of f(x)=(1)/(sqrt(x^2-6x-7)) is (1, 7) [-1, 7] x > -1 or x < 7 ***{x < -1}U{x > 7} (-∞, -1]U[7, ∞) 2. In which of the following is y a function of x?
6. ### Calculus

7) Consider the function f(x)=x2e4x. For this function there are three important intervals: (−∞,A], [A,B], and [B,∞) where A and B are the critical numbers. Find A and B For each of the following intervals, tell whether …
7. ### calculus

Evaluate these limits. (Enter answer as a decimal. Enter INF if the limit is +∞; -INF if the limit is −∞; and DNE if the limit is neither ±∞ and does not exist.) (a) limx→04+x−−−−−√−2x= …
8. ### calculus

You are given that f(x) =1+ax+ax2 f′(x) =−(x+2)ax3 f′′(x) =(2x+6)ax4 and the constant a>0. Write down all intervals on which the function is increasing, decreasing, concave up or concave down. (Enter using …
9. ### Pre calculus

Find the domain of the function. f(x) = -2x + 4 A. (-∞, 0) u(0, ∞) B. (-∞, ∞) C. [-4, ∞) D. (0, ∞)
10. ### Pre calculus

Find the domain of the function. f(x) = -2x + 4 A. (-∞, 0) u(0, ∞) B. (-∞, ∞) C. [-4, ∞) D. (0, ∞)

More Similar Questions