Concept explainers
Relative Extrema
(a) Graph the fourth-degree polynomial
(b) Show that p has a relative maximum for all values of the constant a.
(c) Determine analytically the values of a for which p has a relative minimum.
(d) Let
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Calculus
- Local extrema these exercises involve local maximaand minima of polynomial functions. Graph the function P(x)=(x2)(x4)(x5) and determine how many local extrema it has. If a < b < c, explain why the function P(x)=(xa)(xb)(xc) must have two local extrema-arrow_forwardTorricelli's Law Water in a tank will out of a small hole in the bottom when tank is nearly full than when it is nearly empty. According to Torricelli's Law, the Height h(t) of water remaining at time t is a quadratic function of t. A certain tank is filled with and allowed to drain. The height of Water is measured at different times as shown in the table. (a) Find the quadratic polynomial that best fits data. (b) Draw a graph of the polynomial from part(a) together With a scatter plot of the data. (c) Use your graph from part (b) to estimate how long it takes for the tank to drain completely.arrow_forward37-46 Finding a Polynomial with Specified Zeros Find a polynomial with integer coefficients that satisfies the given conditions. T has degree 4, zeros i and 1+i, and constant term 12.arrow_forward
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