If graph of `y=f(x)` is symmetrical about the y-axis and that of `y=g(x)` is symmetrical about the origin and if `h(x)=f(x)dotg(x),t h e n(d^3h(x))/(dx^3)a tx=0` is cannot be determined (b) `f(0)dotg(0)` 0 (d) none of these

Options

A. cannot be determined
B. `f(0)cdotg(0)`
C. 0
D. none of these

Explanation

To solve the problem step by step, we need to analyze the given functions and their properties.

### Step 1: Understand the properties of the functions
Given that:
- The graph of \( y = f(x) \) is symmetrical about the y-axis, which means \( f(x) \) is an **even function**. Therefore, \( f(-x) = f(x) \).
- The graph of \( y = g(x) \) is symmetrical about the origin, which means \( g(x) \) is an **odd function**. Therefore, \( g(-x) = -g(x) \).

### Step 2: Define the function \( h(x) \)
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