Differentiation questions | form five Pure Advanced Mathematics

(3457) Question Category: Mathematical Calculation

Find the relative maximum and relative minimum values of the function y=frac{x}{1+x^{2}}

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(3458) Question Category: Mathematical Calculation

  1. Use Taylor`s theorem to obtain a series expansion for cos (x+frac{pi}{3}) stating terms up to and including that in x^{3}
  2. Find the minimum and maximum value of 3cosh,x+2Sinh,x

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(3459) Question Category: Mathematical Calculation

  1. If  xsqrt{(1+y)} =ysqrt{(1+x)}=0, prove that frac{dy}{dx}=-frac{1}{(1+x)^2}
  2. Given that f=sin ,xy  find frac{partial f}{partial x}  and frac{partial f}{partial y}
  3. Using Taylor`s theorem, expand sin(frac{pi}{6}+h) in ascending power of h up to h^{4} term and hence evaluate sin 31^{circ}  correct to three decimal places.

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(5353) Question Category: Mathematical Calculation

If the minimum value of f(x)=2x^{3}+3x^{2}-12x+k is one-tenth of its maximum value, find the value of k.

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(5354) Question Category: Mathematical Calculation

  1. If f(x,y)=x^{3}y+e^{xy^{2}}), Find frac{partial f }{partial x} , and , frac{partial f}{partial y}.
  2. If z=x^{2} an^{-1}left ( frac{y}{x} ight ), find frac{partial^2 z }{partial x partial y} at (1,1).

Answer / Solution

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