47) Given, g(x)= lim(t→x)[f(c+t)-f(c+x) ]/(t-x),

Let t-x=h,

so, g(x)=lim(h→0)[f(c+x+h)-f(c+x)]/h,

or g(x)=f'(x+c) [By using first principle of derivative].

Again since f(x) is concave in x, sol clearly it will be concave in (x+c) too.

so g'(x)=f''(x)<=0.

So clearly g(x) is decreasing in x.

"I don't ride side-saddle. I'm as straight as a submarine"