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Let f(x) : (0,00) → (0,0) be a differentiable function, f(1) = 5, f'(1) = 2....
Find the range of the function f(x) = x2 A) (0,0) B)[0,00) C)(1,0) D)(-1,00) E)-, -1] U [0,0] F)RUR G)(1,0) H) (1,-1] Select one: a. F b. C C. B d. H e. D f. E g. A h. G
2. Let g(x) In f(x) where f(x) is a twice differentiable positive function on (0, o) such that f(x + 1) = x f(x) Then for N 1, 2, 3 find g" N+ 2 2. Let g(x) In f(x) where f(x) is a twice differentiable positive function on (0, o) such that f(x + 1) = x f(x) Then for N 1, 2, 3 find g" N+ 2
4. Define the function f: 0,00) +R by the formula f(x) = dt. +1 Comment: The integrand does not have a closed form anti-derivative, so do not try to answer the following questions by computing an anti-derivative. Use some properties that we learned. (a) (4 points). Prove that f(x) > 0 for all x > 0, hence f: (0,00) + (0,0). (b) (4 points). Prove that f is injective. (c) (6 points). Prove that f: (0,00) (0,00) is not surjective,...
The f function differentiable at (-1,4) and 7(3) = 5 also let Hx f'(x) > -1. Find the greatest value f(0).
ame f(x) If f(x) is a differentiable function, find an expression for the derivative of y= X Choose the correct answer below dy 7f(x)-xf'(x) O A. dx 8 X xf (x) 7f(x) dy O B. dx 8 X dy xf(x) 7f(x) O C. dx 8 X 7f'(x) xf(x) dy O D. dx 8 X ame f(x) If f(x) is a differentiable function, find an expression for the derivative of y= X Choose the correct answer below dy 7f(x)-xf'(x) O A....
Note that f is twice differentiable on means that the second derivative f''(x) exists for each x that is an element of Explain in full details! Suppose f is a twice-differentiable function on (0,00) (i.e. f"(x) exists for every 1 € (0,0)), and A = sup \f(x)] = sup{]f(x)]: 0<x<00}, B = sup \f" (x)], C = sup 18" (2)]. O<I<0 0<<< O<I<00 If A+C< show that BP < 4AC. (0,00 We were unable to transcribe this image
Consider the function f(x) = 14x2 + 200 on the open interval (0,00). (1) Find the critical value(s) off on the open interval (0, 0). If more than one, then list them separated by commas. Critical value(s) = Preview (2) Find f''(x) = Preview (3) Looking at f''(x) we can conclude the following: f''(x) > 0 for all 3 on the interval (0,0) and thus we have an absolute maximum at the critical value f''(x) < 0 for all x...
Let f(x) be a differentiable function for all x values and let g(x) Then f(V2) g'(x) = 1 = Select one: f'(V) væ[f(x)]2 f'(V) 2væ[f(V)]2 - f'(V) 21x[f(V)]2 - f'(V) væ[f(Vx)]2 f'(V2) 2[f(VⓇ)]2
Problem 2 (5 points) Let f be a continuous function over R, and let g(x) represent a differentiable function such that 8(2)=- Given that the relationship dt = 29(x)-7 is true for all x, find the following. a) Value of g(1); (2 pts) b) Value of (2). (3 pts)
Question 2 (20 points): Consider the functions f(x, y)-xe y sin y and g(x, y)-ys 1. Show f is differentiable in its domain 2. Compute the partial derivatives of g at (0,0) 3. Show that g is not differentiable at (0,0) 4. You are told that there is a function F : R2 → R with partial derivatives F(x,y) = x2 +4y and Fy(x, y 3x - y. Should you believe it? Explain why. (Hint: use Clairaut's theorem) Question 2...