A Calculus(math) Problem!! Please help me!!!!?

Question

If an even function f(x) has a local maximum

value at x = c, can anything be said about the

value of f at x = −c? Give reasons for your

answer.


This is my question!!

Please help me!!

Thanks!!!

Answer 1

well c stands for any number. can be positive or negative so you dont need the (-) to represent it.

Answer 2

If f(x) = c and f(x) is an even function, we still don't know anything about the value of f(-c).
Consider a 4th degree equation, which has one relative max, one relative min, and one absolute min. By replacing x with (x-h) we can move the graph along the x axis. By adding the constant k to f(x), we can move the graph up or down along the y axis.
So, given f(c), we don't know anything about f(-c) other than it does exist, as the domain for an even funtion is all real numbers.

TO THOSE WHO ARE SAYING EVEN FUNTIONS ARE SYMMETRIC TO THE Y-AXIS: Consider
f(x) = (x-5)^2 [ This is symmetric about x = 5, not the y=axis]

Answer 3

If the even function is of degree 2 , then nothing can be said.

If the even function is of degree 4 and has just one local maximum, then nothing can be said. If however the function has two local maximums, then one will be at c and the other at -c.

This is an interesting problem and requires more study to provide you with all the conditions and restrictions on an even function.

Answer 4

An function f is called even if f(-x) = f(x) for all x in the domain of the function.

If you draw a graph, placing one dot on the right side of the y axis, then another dot has to be placed a mirror image on the left of the y axis.

Therefore if it is a local maximum on the right, it has to be as local maximum on the left.

Answer 5

Think of functions that are symmetric to the x-axis, but with a maximum point, denoted by c. The value -c will be either inessential or the minimum or the maximum as well...
Think of circles and ellipticals.

Answer 6

At x=-c, the function will have a local maximum, because the function is even in nature.

its graph will be symmetric to the y-axis.

Answer 7

If the function has a mirror image across the x-axis then
x= -c would be the local minimum.

Answer 8

if F(x) = F(-x) then function is even
hence at x= -c it will have max. value only.