# calculus

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).

1. Steve

(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.

## Similar Questions

1. Reactions follow the law of conservation of mass. a.) True b.) False Answer: True 2. Reactants are the materials used in a chemical reaction. a.) True b.) False Answer: True 3. In a chemical equation, the mass on the left of the …

can you help me thank you: 2.Detecting bias is one of the major keys to effective critical thinking and reading. True or False, I believe True 3.Deductively valid arguments can guarantee their conclusions. True or False, I believe …
3. ### calculus

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) the function f(x)=3/2 +cx^-2 is a solution of the differential equation xy'+2y=3 b) …
4. ### English12

Below, you will find a list of sentences. After each sentence, select true if the topic of the statement is suitable to form the basis of a single persuasive paragraph. If the topic of the statement in your textbook is unsuitable for …

Fats help maintain your cell membranes. (1 point) True False 12. Your body does not use energy when you sleep. (1 point) True False 13. People with anorexia nervosa eat large amounts of food and then purge. (1 point) True False 14. …

True/False Indicate whether the statement is true or false. 11. A person with good self-esteem is willing to try new things. (1 point) True False 12. Stress can be positive or negative. (1 point) True False 13. Giving away prized possessions …
7. ### 7th grade health true or false

11. Disagreements are a normal part of life. (1 point) True False 12. Talking to a trustworthy adult is the best way to stop sexual abuse and get help. (1 point) True False 13. Some conflicts are made worse by peer negotiation. (1 …
8. ### Physical Ed

11. Disagreements are a normal part of life. (1 point) True False 12. Talking to a trustworthy adult is the best way to stop sexual abuse and get help. (1 point) True False 13. Some conflicts are made worse by peer negotiation. (1 …
9. ### French Check Ms. Sue

Please check this. Thank you! 1. France is a country in Asia. true false*** 2. There are many countries in Africa where French is one of the principal languages of the people. true false 3. Québec, in Canada, is a French speaking …
10. ### Computer science

While you can pass only one argument into a function, you can return as many values as needed from a function. True False A library function saves time for the programmer because it allows for code reuse. True False Each function should …

More Similar Questions