Let f(x) be a func. satisfying f(-x)=f(x) for all real x. if f"(x) exist, find its value.

Step-by-step explanation:

A function satisfying the equation is said to be an even function. This denomination comes from the fact that the same relation is satisfied for functions of the form with even. Observe that if is twice differentiable we can derivate using the chaing rule as follows:

implies

Applying the chain rule again we have:

implies

So we have that function is also an even function.

here is a big fat