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Determining the Differentiable of the function f(x) How do you do all the questions?
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
It is known that f :(0,2) + R is a differentiable function such that \f'(x) < 5 for all x € (0,2). Now let bn := f(2 – †) for all n € N. Prove that this is a Cauchy sequence.
It is known that f :(0,2) + R is a differentiable function such that \f'(x) < 5 for all x € (0,2). Now let bn := f(2 – †) for all n € N. Prove that this is a Cauchy sequence.
4 Suppose f : (0,0) → (0,x), is a differentiable function satisfying f(a +b)-f(a)fb), for all a,b>0 Moreover, assume that f(0)1 (a) Prove that there exists λ (not necessarily positive) such that f(r) = e-Ar, for all r. Hint Find and solve a proper differential equation. (b) Suppose that X is a continuous random variable, with P(X>ab)-P(>a)P(X> b), for all a, b e (0, oo). Prove that X is exponentially distributed
For the function f(x), determine whether or not f is continuous and/or differentiable at the following points. Also using only the given function (not a graph), determine what occurs graphically at these points. f(x) = 1, X, x² - 12, x < 0 0<x< 4 X > 4 (a) At x = 0, f(x) is ---Select--- . At this point, the graph of f(x) has ---Select--- (b) At x = 2, f(x) is ---Select--- . At this point, the graph...
Suppose that f(x) is a differentiable function such that the tangent line at x = 3 is given by y=-***. How many of the following statements MUST be true? I. According to the linearization of fat x = 3. f3.001) - 0.9989 IL (3) -0. III. f is concave down on an open interval containing x = 3. IV. The graph of y = f(x) attains a maximum value on the interval (-1,4). V. Applying Newton's Method to approximate the...
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....
Can you find a differentiable function f(x) defined on the
interval [0, 3] such that
,
and
for all x ∈ [0, 3]? Justify your answer (do not write only Yes or
No, but explain your answer).
We were unable to transcribe this imageWe were unable to transcribe this imagef'(x) <1
True or False If f is differentiable everywhere and f^′(x)<0 for all x, then lim x→∞ f(x)= −∞
3. (a) Let f be an infinitely differentiable function on R and define х F(x) = e-y f(y) dy. Find and prove a formula for F(n), the nth derivative of F. (b) Show that if f is a polynomial then there exists a constant C such that F(n)(x) = Cem for sufficiently large n. Find the least n for which it is true.