How to find these Polynomial features?

I'm having trouble figuring out the:

A.) Total number of 'turning points'

B.) End behavior

C.) X-intercepts (in coordinate form)

D.) Y-intercepts (in coordinate form)

E.) (x,y) coordinates of the local maxima and minima

F.) Intervals of increasing and decreasing behavior

The polynomial number is f(x) = 7 + 10x^7 + 19x^5 + 9x^3 + 6x

Thankyou(:

1 Answer

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  • 7 years ago
    Best Answer

    A) A graph takes a turn whenever dy/dx is equal to zero. Thus, total number of turning points is equal to the number of values of x for which dy/dx is zero.

    First we find dy/dx. dy/dx=0+70x^6+95x^4+27x^2+6

    Now put this equal to zero. And find the real values of x.

    WHEN WE SOLVE THIS, WE FIND THAT THIS EQUATION CANNOT HAVE ANY REAL VALUE OF X FOR WHICH DY/DX IS ZERO. THEREFORE, THERE IS NO TURNING POINT.

    B) After finding the last turning point, check weather is it decreasing or increasing function. And accordingly describe its behaviour.

    NO TURNING POINT, SO JUST SUBSTITUTE TWO VALUES OF X (LIKE -5,5) SO AS TO KNOW THE GENERAL BEHAVIOUR. WE NOTICE THAT IT GOES TO +INFINITY ON Y AXIS.

    C) X-intercept, would be when Y=0. i.e. put f(x)=0. and find values of x.

    In co-ordinate form would be (-0.59,0).

    D) Y-intercept, would be when X=0. i.e.f(0)=7.

    In co-ordinate form would be (0,7).

    E) NO

    F) ALWAYS INCREASING.

    a0=2&a1=7 + 10x^7 + 19x^5 + 9x^3 + 6x&a2=7 + 10x^7 + 19x^5 + 9x^3 + 6x&a3=&a4=4&a5=1&a6=8&a7=1&a8=1&a9=1&b0=500&b1=500&b2=-5&b3=5&b4=-1&b5=20&b6=10&b7=10&b8=5&b9=5&c0=3&c1=0&c2=1&c3=1&c4=1&c5=1&c6=1&c7=0&c8=1&c9=0&d0=1&d1=20&d2=20&d3=0&d4=&d5=&d6=&d7=&d8=&d9=&e0=&e1=&e2=&e3=&e4=14&e5=14&e6=13&e7=12&e8=0&e9=0&f0=0&f1=1&f2=1&f3=0&f4=0&f5=&f6=&f7=&f8=&f9=&g0=&g1=1&g2=1&g3=0&g4=0&g5=0&g6=Y&g7=ffffff&g8=a0b0c0&g9=6080a0&h0=1&z

    COPY THE ABOVE GRAPH PATH(remove all white spaces) ON THE FOLLOWING WEBSITE,

    http://rechneronline.de/function-graphs/

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