if f(x) = Va --1, then f is differentiable on the interval Select one: o (1,00)...
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
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
9. Suppose that f : [0,-) + R is differentiable and that the derivative f' : [0,00) + R is also differentiable, with f(0) = f'(0) = 0. Suppose also that [f"(x) < 1 for all € [0, 0). a) Show how the Mean Value Theorem can be used to prove that f(x) <r? for all x € (0,00). b) Show how the Cauchy Generalized MVT can be used to prove a stronger statement: |f(7) < 2 for all 2...
Let f(x) : (0,00) → (0,0) be a differentiable function, f(1) = 5, f'(1) = 2. Let g(x) = xf (:22). Find g'(x) and evaluate g(1) and g'(1).
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
Question 4 (1 point) if f(x) is a one-to-one differentiable function with f(a) f'(a) +0, then f'(0) (-)'(a) = 1. = band True False Question 5 (1 point)
Determine the domain of each of the functions P(x), Q(x), V(x), and Z(x). Select the one row that gives the correct domain underneath each function. P(x)= x2 + 1 Q(x) = Ne + 1 V(r) = **1 Z(x) = log (x + 1) OP: [-1, )Q: (-00, -1) (-1,00) V:(-0,0) Z: (-1,00) OP: (-00,00) Q: (-1,0) V: (-00, -1) (-1,0) Z: (-1,00) OP: (-00,00) Q: (-1,-) V: (-0, -1) U (-1,00) Z: (-1,0) OP: (-0, -1) U (-1,0) Q: (-1,-)...
The function f that satisfies f'(x) = 3x2 +1, f(2)=5 is Select one: a. f(2)=23+ O b. f(x) = 2 + 1 - 5 O c. f(x)=x3 ++2 d. f(x) = 3x2 – 7 O e. None of these. Let f(2) be a function that is continuous on 1, 7] with f(1) =3 and f(7) = 9. Then the Intermediate Value Theorem guarantees that Select one: O a. f'(2)=1 has at least on solution in the open interval (1,7). O...
Let if x<o if o sxs1 <xs 2 f(x) = O NO 2 - X lif O VIVA x and g(x) = f(t) dt JO (a) Find an expression for g(x) similar to the one for f(x). if x < 0 if o sxs 1 g(x) = 3 if 1 < x 2 if x > 2 (6) Sketch the graph of f. Sketch the graph of g. (c) Where is differentiable? (Enter your answer using interval notation.) Where is...
True or False: If f(x) and g(x) are two differentiable functions on an interval (a,b), and f(x)>g(x) on (a,b), then f'(x)>g'(x).