Use the equation ƒ(x) = ƒ(a) + ƒ′(a)(x - a) + ƒ′′(c2) /2 (x - a)2 to establish the following test. Let ƒ have continuous first and second derivatives and suppose that ƒ′(a) = 0. Then a. ƒ has a local maximum at a if ƒ′′<= 0 throughout an interval whose interior contains a; b. ƒ has a local minimum at a if ƒ′'>= 0 throughout an interval whose interior contains a.

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Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: Given, f(x)=1x, a=0.9 now find linearization f(0.9)=10.9=109 so linearization at 910,109…

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Q: A:- Find the orthogonal trajectories for functions In -1) = - COS X +a y

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Q: Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 2 at x = −2 and a…

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A: Critical points using second derivative test