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if f(x) =(x^2-3x+2) /(x^2-7x+12) then number of extrema for g(x) where g(x) =f(IXI)

if f(x) =(x^2-3x+2) /(x^2-7x+12) then number of extrema for g(x) where g(x) =f(IXI)

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1 Answers

Aditya Gupta
2080 Points
2 years ago
to draw graph of g(x), we simply draw the graph if f(x) in right half of coordinate plane and then reflect it onto the left hand side (reflection about y axis).
now, to draw graph of f(x), we first draw the sign scheme, then find f’(x), and draw its sign scheme as well. also, we observe that f(x) has exactly 2 extremas when x greater than zero. so g(x) has 4 extremas (due to reflection). however, g(x) will also have an extrema at x=0 since it has to abruptly change its slope there to the exact opposite of rhs (note that even though this is an extrema, g(x) is not differentiable at x=0). hence there are 5 extremas of g(x) in total

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