[K4] Determine an equation, in simplified form with no radicals (V ), for the family of 1 cubic functions with zeros -2±2/3, and 4
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![[K4] Determine an equation, in simplified form with no radicals (v), for the family of
1
cubic functions with zeros -2 ±2/3, and
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- For which values of c does f (x) = x2 + cx + 1 have a double root? No real roots?-x+y=11 5x-6y=2 solve by elimination but start with eliminating the x terms first. show all workFind the smallest value of the positive constant m that will make mx - 1 + (1/x) greater than or equal to zero for all positive values of x.
- The subpart “d” needs to be solved. f(g(1))Starting with x 1 = 2 find the third approximation x 3 to the root of the equation x3 - 2x - 5 = 0Find two explicit functions by solving the equation for y in terms of x, (b) sketch the graph of the equation and label the parts given by the corresponding explicit functions, (c) differentiate the explicit functions, and (d) find dy dx implicitly and show that the result is equivalent to that of part (b). x2 + y2 − 4x + 6y + 9 = 0
- A car moves along a straight road in such a way that its velocity (in feet per second) at any time t (in seconds) is given by v(t) = 3t(square root) 9-t2 (0 ≤ t ≤ 3). Find the distance traveled by the car in the 3 sec from t = 0 to t = 3.Find the nth Maclaurin polynomial for the function f(x) = cos 3x, n = 4Make an equation for f(x) and g(x) - f(x) has the y-intercept of 3 - g(x) has one reflection over the x -axis, is vertically stretched by a factor of 5 and translated up 3 units - f(x) and g(x) share a common characteristic: a y-intercept of 3
- Solve using Reduction of Order. (D^2-1)y=2e^x(2) For the f(x)=−x^3+3x+6 determine the coordinates of the turning point(s) and any point(s) of inflection,if they exist.Suppose that the distance an aircraft travels along a runway before takeoff is given by D = (10/9)t2, where D is measured in meters from the starting point and t is measured in sec-onds from the time the brakes are released. The aircraft will become airborne when its speed reaches 200 km/h. How long will it take to become airborne, and what distance will it travel in that time?