Posted by **help please.** on Sunday, March 11, 2012 at 12:03pm.

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.

a- if f is a function of x and y and a is a real number, then f(ax, ay)= af(x,y).

b- if fx(a,b) < 0, then f is decreasing with respect to x near (a,b).

- calculus -
**Steve**, Sunday, March 11, 2012 at 1:35pm
(a) is certainly not true in general. While it is true for linear functions, it is otherwise not true.

f(x,y) = x^2/(y^2+1)

f(ax,ay) = (a^2x^2)/(a^y^2+1)

or

f(x,y) = sin(x+y)

f(ax,ay) = sin a(x+y)

or

f(x,y) = e^x * ln(y)

f(ax,ay) = a^ax * ln(ay) = e^a * e^x * (lna + lny)

(b) I assume fx means the partial with respects to x. That's true. The derivative is the slope of the curve in the intersection of f(x,y) and the plane y=b.

## Answer This Question

## Related Questions

- calculus - determine whether the statement is true or false. If it is true, ...
- 7th grade health true or false - 11. Disagreements are a normal part of life. (1...
- Physical Ed - 11. Disagreements are a normal part of life. (1 point) True False ...
- 7th grade health Ms. Sue please thanks - True/False Indicate whether the ...
- math - Algebra For questions 1-5, find the value of the variable. 1. x = (1 ...
- Science - 1. Scientists are not concerned with the human impact on the ...
- Calculus - Determine whether the statement is true or false. If it is false, ...
- math - Indicate whether each statement is true or false by checking the ...
- Chemistry: Answer check please! - 1. Reactions follow the law of conservation of...
- math - Indicate whether each statement is true or false by checking the ...

More Related Questions