Consider the functions fi(x) = x and f2(x) = 5-9cx on the interval [0, 1]. (a) Find the value of the constant c so that fi and f2 are orthogonal on [0, 1]. (b) Using the value of the constant c from part (a), find the norm of f2 on the interval [0, 1].

18 > (a) Find the direction for which the directional derivative of the function f (x, y) = 7xy² + 5x² is a maximum at P = (-1,2). (Use symbolic notation and fractions where needed. Give your answer in vector form.) direction: (b) Find the maximum value of the directional derivative. (Use symbolic notation and fractions where needed.) ||Vf(-1,2) || =

Let f(w)f(w)be a function of vector ww, i.e.   f(w)=1/(1+e−wTx). Determine the first derivative and matrix of second derivatives of ffwith respect to w ?

Q 2.8 Consider the functions f₁(x)=x and f₂(x)=3-5cx on the interval of [0,1]. so that a) Find the value of the constant c f, and £₂ are orthogonal on [0, 1]. Your answer should be symbolic and should not have any decimals ) Using the value of the constant c from part(a), find the norm of f₂ on the interval '[0, 1];