Question

If we have f(x) to be an even function and f'(x) to be odd function what can you say about the nature of function f(x)?

Answer 1

Is it right to say that it might be exponential function or trigonometric or even polynomial function?

Answer 2

Could be parabolic...well by saying exponential/trig/even we might distort the whole idea of its being unique and solvable...we can make infinite arguments then...better be a parabolic (ax2 +bx+c)

Answer 3

Not exponential actually..
But we can say it is trigonometric.
For eg cosx

Answer 4

@welshfella

Answer 5

I would say definitely a trig function - you quoted cos x which is even and -sin x which is odd.
I dont think an exponential.

Answer 6

It can be even a polynomial function as well .
For example 2x^4+3x^2

Answer 7

When is this not true for differentiable functions?!