f (x) = 2x² + 12x + 15 as x → -0f (x) → -∞ as x → -o f (x) → - as x → +0 f (x) → -0 as x →+o (x) → + Ов - -0∞ f (x) → +∞ f (x) as x -o f(x) → t∞ as x as X → +0o f (x) as x -+00
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- If g(y) is differentiable for 2<_y<_3 (<_ means less than or equal) and g(2) =g(3)=-1, then there is some 2<_a<_3 such that g'(a)=0 true or falseFind the location of the global maximum and minimum of f(x) = x^3-6x^2+1f(x)=x3−6x2+1 on the interval [-1,7][−1,7]. a) The global maximum is attained at x = 0x=0 and the global minimum at x = 4x=4. b) The global maximum is attained at x = 7x=7, but there is no global minimum. c) The global maximum is attained at x = 0x=0 and the global minimum at x = -1x=−1. d) The global maximum is attained at x = 0x=0, but there is no global minimum. e) The global maximum is attained at x = 7x=7 and the global minimum at x = -1x=−1. f) The global maximum is attained at x = 7x=7 and the global minimum at x = 4x=4.4.) Snow being produced by a snow machine is blown onto a ski mountain at a rate modeled by S(t) measured in cubic feet per hour, where t is measured in hours. At the same time, because of unseasonably warm temperatures, snow is melting at a rate modeled by M(t) measured in cubic feet per hour, where t is measured in hours. The functions S and M are nonnegative and differentiable for all times t. Which of the following inequalities indicates the rate of change of the total number of cubic feet of snow on the mountain is decreasing at time t? A.M(t)
- f(x) = (x2-x-1) e-x is restricted to the domain x ≥ 0 and it has two critical points. One at x = 0 and the other at x = 3 At what value x does f(x) attain its maximum?The function f(x)=(a-x)2/3 has domain R and only one critical point x= a.Use a number line to find the interval(s) on which the function is increasing.Use algebraic methods to determine the critical value(s) of f(x)= x/(x^2-x-2). Give your answers in exact form.