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In Problems 21-28, determine whether
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Fundamentals of Differential Equations and Boundary Value Problems
- please help with this composite functions questionarrow_forwardSuppose that f:R → R is a function with second derivative f"(x)=x•(x+ 1)³ • (x + 5)ª . Find intervals of concavity-up and concavity-down of f(x), and the x-coordinate(s) of any point(s) of inflection. Explain your answers.arrow_forwardLet f be a function on [0, 7] whose second order derivative is continuous and f(T) = 1. Suppose that | (f(2) + f"(x)) sin a da = 4. Compute f(0).arrow_forward
- 7. Draw the function (f(x) = cosx sin (x) and its derivative in one graph for the same range for x where TT S X = t - the first has a separate line and the second is a dashed line with the addition of the illustration square and the names of the function axesarrow_forward7. Determine where the function is continuous. (a) f(x) = 1+x (b) g(x) = sinx+x² + x + 1. x² (c) h(x) = 2x x+21arrow_forward4. Let f be the function given by f(x) = 4 - x. g is a function with derivative given by g'(x) = f(x)ƒ'(x)(x - 2). On what intervals is g decreasing? a. (-∞0, 2] b. [2,00) C. [2,4] [4,00)arrow_forward
- Consider the graph of the function f given below. f(x) -2 -4 B) If h(x) = 2 0 2 X 4 A) If g(x) = xƒ(x), calculate g' (3). [Select] x² ƒ(x)' C) If i(x) = x² ƒ(x), calculate ¿" (−1). [Select] calculate h' (−1). [Select]arrow_forward5 Suppose this graph represents the function x). At what value(s) of x does f'(x) > 0 and f"(x) = 0? A -1 -2 1 2 0. 6 Suppose this graph represents the function fx). For what value(s) of x does f"(x) = 0 and f"(x) < 0? A -1 -2 1 2arrow_forward(a) Which of the following are functions? If f is not a function explain why. i. f :R →R with f(x) = ii. ƒ :Z → Z with f(x) = iii. f :R → R with f(x) = ln(x) (b) Let f : R → R and g : R → R with f(x) = x + 2 and g(x) = -x. Find gof, (go f)-', f-' and g- (c) Let f : R* → R with f(x) = , where R* is the set of all real numbers different from 0. i. Determine whether or not f is a one to one function ii. Determine whether or not f is an onto function (d) Given a function F : P({a,b,c}) → Z is defined by F(A) = |4| for all A E P({a,b, c}). i. Is Fa one-to-one function? Prove or give a counter-example. ii. Is F an onto function? Prove or give a counter-example. (e) Let f : A → B and g : B → C be functions. Prove that if go f is one-to-one then f is also one-to-one.arrow_forward