Homework Help: Math

Posted by Hannah on Saturday, February 26, 2011 at 3:46pm.

Which of the following could represent a function having the given properties?

1)increasing slope for x<4
2) f'(x)>0 for all x(x cannot =4)
3)asymptote at x=4.

Again I know we cannot graph but how can I figure this out?

Math - MathMate, Saturday, February 26, 2011 at 4:30pm
Asymptote at x=4 indicates a factor of (x-4) in the denominator.

Let's try f(x)=1/(x-4)

f'(x)=-1/(x-4)²
so f'(x)<0 for all x except 4.

Let's try f(x)=-1/(x-4)
f'(x)=1/(x-4)² >0 for all x.

Check f"(x)=2/(x-4)³
f"(x)>0 ∀x<4.

So all conditions are satisfied.

Answer this Question

Related Questions

Math - which of the following graphs could represent a function with the ...
calculus - In the following problem, suppose f(x) is continuous (and ...
Precalculus - Write an equation for rational function with given properties. a...
MATH EMERGENCY - Given Equation AX + BY + C = 0, which following conditions ...
another graph - complicated - Sketch the graph of a differentiable function y = ...
CALCULUS - Find the x-coordinate of the absolute minimum of f(x) = x^3 - x^2 - x...
Algebra - Im having a hard time figuring out this problem: Use the function, y...
college trig - I need to find the domain of the following function: y=arcsin((x-...
college algebra - Given the following rational function, find a. the horizontal ...
Calculus - Sketch a possible graph for a function that has the following ...

For Further Reading

First Name:
School Subject:
Answer: