calculus 4 problems

Find the equation of the curve that passes through the point (3,- 4) such that the slope of the tangent at the point (x, y) on it equals ..

If Mean value theorem is applicable, solve the equation Show that one of the roots lie in the open interval (a, b). This verifies the Mean Value Theore..

Let f be a continuous function on an interval I = [a, b]. Then, f has the absolute maximum value and f attains it at least once in I. Also, f has the absolute minimum value and attains it at least once in ..

Equation of the normal at (x 1 ,y 1 ) is o..

If y = f(x) is differentiable then is called the first order derivative of y = f(x) if is further differentiable the is called the second order derivative of f(x).Derivatives of standard functions ..

Every rational function is continuous at each point of its domai..

Verify mean value theorem for the function f (x) = (x - 4) (x - 6) (x - 8) in [4,..

2 < e < 3 The value of e rounded off to four decimal places is 2.7183. For complex numbers x,y, we have e x + y = e x y y . For any rational number x, the sum, e x , of the series ..

f ' (x) = (x - 6) (x - 4) + (x - 4) (x - 8) + (x - 6) (x - 8) f '(x)= (x 2 -10x + 24) + (x 2 - 12x + 32)+ (x 2 - 14x + 48) = 3x 2 - 36x + 104 f '(x) is defined for all values on the interval (4,10). \ f '(x) is differentiabl..