calculus

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Iamhaving a really hard time trying to understand this question. Can someone please show me how to work this question.

Give the following polynomial, find
a. the zeros and the multiplicity of each
b. where the graph crosses or touches the x-axis
c. number of turning points
d. the end behavior

f(x)=(x-1)(x-5)

please show work.

  • calculus -

    u=x-1 dx=du
    v=x-5 dx=dv
    f=uv
    f'=uv'+vu'=(x-1)+(x-5)=2x-6

    zeroes: f(x)=0 at x=1,and x=5
    f"=2 means it is always increasing, no inflection point.
    end behaviour: at x=+- inf, f(x)=+ undef

  • calculus -

    one small item:

    f" > 0 means its always concave up, not increasing. Its slope is always increasing.

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