Let f(x) be any function continuous and twice differentiable function on (a,b) . If for  all x∈(a,b),f'(x)>0 and f''(x)<0, then for any c∈(a,b),f(c)-f(a)f(b)-f(c) is greater  than

Since f'(x)>0, the function f is increasing and since f"(x)<0, the function downward facingNm So, slope of AC will be greater than slope of BC i.e., f(c)-f(a)c-a>f(b)-f(c)b-c⇒f(c)-f(a)f(b)-f(c)>c-ab-c