N=3
Sketch the graph of the function f(x) below for your particular value of N. Indicate if a given function is even or odd (if applicable); find the points of discontinuity (if any). Determine y- and x-intercepts and the intervals where the function is positive or negative. Then determine x,y-coordinates of the critical point(s), maxima and minima, x,y- coordinates of the inflection point(s), intervals of rising and falling, intervals of concavity up and down, domain and range. Indicate if there are any asymptotes. (See the sample file Quiz 6c1 H_MTH 1220 1260 1009_for_N-50_ans.doc.) 3 f(x)-(4-N5)x2 (4N/5-4)x-4N/5 Directions. (When evaluating the coefficients (4 - N/5) and (4N/5 -4) remember the order of operations: do first the division and only then - subtraction. Check at least twice all the coefficients and the constant.) The point x1-N/5 represents one of the roots of the third-degree algebraic equation f(x) 0; in other words, t is one of zeros of the polynomial function f(x). Now use the polynomial FACTOR THEOREM (xi is zero of Pa(x) if and only if (x xi) is a factor of P(x)) to present the given function as fx)- P3(x) = (-x)(ax2 + bx + c). The-coefficients a, b, and the constant c in the trinomial in () can be determined as a result of the procedure of long division of the polynomials Ps(x)/(x-x) = ax2 + bx + c. (See the file Long division of polyno mials.doc. Be attentive with signs: the number xi in the binomial (x -xi) is negative.)