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How do you find 10 derivatives for clamor?
Clamor derivitives
Why are graphs of polynomials smooth and continuous?
Smooth function has derivatives of all orders. Polynomials have derivatives of all orders, thus polynomials are smooth functions. For example: f(x)=2x+3 => f'(x)=2 => f''(x)=0 => f'''(x)=0... So all derivatives exist. (Derivative being zero is ok.) Their continuity can be proven using the Weierstrass (epsilon-delta) definition.
What is the formula of bordered Hessian matrix?
The bordered hessian matrix is used for fulfilling the second-order conditions for a maximum/minimum of a function of real variables subject to a constraint. The first row and first column of the bordered hessian correspond to the derivatives of the constraint whereas the other entries correspond to the second and cross partial derivatives of the real-valued function. Other than the bordered entries, the main diagonal of the sub matrix consists of entries for the second partial derivatives. All other entries of the sub matrix off of the main diagonal correspond to all combinations of cross partials. Evaluating the determinant of the bordered hessian will allow one to determine if the function attains its maximum or minimum at the stationary points, which by the way are limited in the fact that they must both satisfy the gradient equations and the constraint.
Find the derivatives of all orders of the functions y x42-32x2-x?
y=x^42-32x^2-x y' = 42x^41 - 32(2)x - 1 y' = 42x^41 -64x-1
What is the simplified expression for 1 plus radical 5 over 5 plus radical 5?
The trick here is to multiply by the value 1, but express it as (5 - √5)/(5 - √5). This forms a difference of squares on the bottom, eliminating the radical:(1 + √5) / (5 + √5)= (1 + √5)(5 - √5) / (5 + √5)(5 - √5)= (5 - √5 + 5√5 - 5) / (25 - 5√5 + 5√5 - 5)= 4√5 / 20= √5 / 5
