Insurance and Annuity

At any point P(x₁

At any point P(x₁, y₁) on curve y = f(x), the slope of tangent = dy/dx|(x₁,y₁) and slope of normal = -1/(dy/dx)|(x₁,y₁). Equation of tangent: y - y₁ =

Derivatives measure instantaneous rates of change

Derivatives measure instantaneous rates of change. If two quantities x and y are related by y = f(x), then dy/dt = (dy/dx) × (dx/dt). For related rate

For a differentiable function f(x)

For a differentiable function f(x), the approximate value at x = a + h is given by f(a + h) ≈ f(a) + h × f'(a). This method is useful for calculating

If function f is continuous on

If function f is continuous on [a,b], differentiable on (a,b), and f(a) = f(b), then there exists at least one point c in (a,b) where f'(c) = 0. Geome

If function f is continuous on

If function f is continuous on [a,b] and differentiable on (a,b), then there exists at least one point c in (a,b) where f'(c) = [f(b) - f(a)]/(b - a).