If x= m-2 and `x/m - (x+1)/m =1` , find 'm'

If f(x) = log ((m(x))/(n(x))), m(1) = n(1) = 1 and m'(1) = n'(1) = 2, " then" f'(1) is equal to

f(x) = |x-1| + |x-2|, g(x) = x+(1)/(x), x gt 0 if m_(1) = min (f(x)) and m_(2) = min (g(x)) , then (m_(1)+m_(2))/(m_(2)-m_(1)) is equal to_________.

If m and x are real numbers where m in Ie^(2mi cot^(-1)x)((x.i+1)^(m))/((x*i-1)^(m))

If x^m y^n = (x+y)^(m+n) then find (dy)/(dx) at x=1, y=2

Let f(x) = (x^(2) + 4x + 1)/( x^(2) + x + 1), x inR If m le f(x) le M AA x in R , then (1)/(2) (M - m) = _______

If y+3=m_1(x+2) and y+3=m_2(x+2) are two tangents to the parabola y_2=8x , then (a)m_1+m_2=0 (b) m_1+m_2=-1 (c)m_1+m_2=1 (d) none of these

If the maximum and minimum value of (sin x-cos x-1)(sin x+cos x-1)AA x in R is M and m the n find value of (M-4m)

If m and M respectively denote the minimum and maximum of f(x)=(x-1)^(2)+3 for x in[-3,1], then the ordered pair (m,M) is equal to