Consider the function f : R³ R defined by f(x, y, z) = tanh(5x² + 2y² − 3z²) and the point P : (x, y, z) = (1, 1, 1). (a) In what direction is ƒ most rapidly increasing at the point P? (b) Calculate the directional derivative of f in the direction of u = (c) Determine an expression for the linear approximation ƒ of ƒ at point P. (d) Use the linear approximation to approximate the value of ƒ(1,-1, 1). N = (2, -1, 2) at the point P.

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Q: at the point

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