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)` at x=0 is (a)cannot be determined (b) `f(0)dotg(0)` (c)0 (d) none of these

Options

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

Explanation

y=f(x) is an even function and y=g(x) is an odd function.
`"or "h(x)=f(x) g(x)` is an odd function.
`"or "h(x)=-h(-x)`
`therefore" "h''(x)=-h''(-x)`
`"or "h''(x)=-h''(-x)`
`"or "h'''(x)=h'''(-x)`
Now, we cannot determine the value of h'''(0).