Math, asked by honeysinghaa, 10 months ago

The function f(x)=(x-1) |x^2-3x + 2| +cosx
(x). is not differentiable at **​

Answers

Answered by Agastya0606
2

Given: The correct function is f(x)=(x²-1) mod( x² - 3x + 2 ) +cos mod( x )

To find: The given function is not differential at?

Solution:

  • Now lets write the given function:

              f(x)=(x²-1) mod( x² - 3x + 2 ) + cos mod( x )

  • So now, let us consider two functions: g(x) and h(x)

             g(x) = (x²-1) mod( x² - 3x + 2 )

             h(x) = cos mod( x )

  • So eventually h(x) becomes:

            h(x) =  g(x) + h(x)

  • Now consider the function h(x) = cos mod( x )
  • As we know that mod(x) is x when x≥0 and -x when x<0
  • So cos mod(x) will be cos x when x≥0 and cos(-x) when x<0
  • But we know that cos(-x) = cos x,

                        so it becomes cos x ∈ R. As the graph of cos x do not have any sharp point so it is always differentiable.

  • Now lets consider g(x) = (x²-1) mod( x² - 3x + 2 )
  • Solving this,

                g(x) = (x-1)(x+1) mod((x-1)(x-2))

                g(x) = (x-1)(x+1) mod(x-1)mod(x-2)

  • So the critical points are: 1, -1, 2

             When x≤-1, g(x) will be positive.

             When -1<x≤1, g(x) will be negative.. that is -g(x)

             When 1<x≤2, g(x) will be positive.

             When x>2, g(x) will be positive.

  • So we can see that graph is not changing in third and fourth case, so the function is not differentiable at 2.

Answer:

             So the function is not differentiable at 2.

Answered by andromedaproximapi
0

Answer:

x = 2

Step-by-step explanation:

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