Let fand g be twice differentiable functions such that f'(x) S 0 for all x in the domain of f. If h(x) = f{g'(x)) and h'(2) = 4, what (if anything) can you say about f, g, and h at x = 2? %3D

Q: We note that F is continuous for all x, and its derivative is (x-1) if x>0 F'(x)= -1 if xr<0 The…

A:

Q: Suppose F(x) is a differentiable function for all real numbers x. Evaluate the following derivative.…

A: We have to find the derivative of the function, using dxndx=nxn-1

Q: Use the definition to calculate the derivative of the criterion of the function f(x) = e14x. In…

A:

Q: If a continuous, differentiable function f is equal to 2 at x = 3 and at x = 5, what can you say…

A: Given f(x) is continuous and differentiable and f(3) = f(s) = 2Concept Roll's Theorem If f(x) is…

Q: 3. FIND THE DERIVATIVE BY THE LIMIT PROCESS OFf(x) = Vx+2.

A:

Q: Consider a function f with domain {x|x 0} and the following derivatives: f'(x) = x2 4x - a and f"…

A:

Q: Determine if the function f(x)= is continuous -- sin(x) x on the interval I= (0,1).

A:

Q: Suppose that the FIRST DERIVATIVE of a function f is given by f' (x) = (x – 3)² (z² + 5x). Find the…

A: We find the critical numbers by solving f'(x)=0

Q: The critical numbers z = 1 and x = -2 are found from a continuous function f' (z). Given that the…

A: The Solution is given below

Q: The stock price for a certain corporation can be approximated for the years 2009 through 2015 by…

A: In this question we are given with the function and we have to find the minimum stock price which we…

Q: is there any linear independent functions with n – 1th continuous derivative g1, 92, ... , gn(with…

A:

Q: Show that r sin (1/x) fails to have a derivative at r = 0 and even the one-sided limits (lim,-0+ (f…

A: We will prove the given statement.

Q: a. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and…

A: fx=xlnx Differentiating with respect to x, we get f/x=dxdxlnx+dlnxdxx    Because,…

Q: Suppose h is a twice-differentiable function such that it has second derivative given by the formula…

A:

Q: 1. Show that a frination fiłamb ]->1R is differentiable at xolamb) is and only if its lower and…

A: Solution: f:[a,b]→ℝ is differentiable at x0(a,b). Let us take upper derivative at x0+. Then,…

Q: Find the critical points of the following function on the given interval. Identify the absolute…

A: Given function:                                  g(x)=-12sinx+12sinxcosx    on 0, 2π   Let's take…

Q: ) Suppose f (x) is continuous on [0, 2] and differentiable on (0,2). Suppose f (0) = 3 and f (2) =…

A: Use the concept of Roll's Theorem and Extreme Value theorem and solve the problems.

Q: Since f'(x) > 0 when x 0 (x 1), f is increasing on the intervals (--, -1) and and decreasing on the…

A: Given that: f'(x)=-4x(x+1)2(x-1)2

Q: Find the critical points of f(x) and use the Second Derivative Test (if possible) to determine…

A:

Q: 7. If a continuous, differentiable function f has zeroes at x = -4, x = 1, and x = 2, what can you…

A: Mean value theorem relates average rate of change of a function over an interval to its…

Q: 2 Find the derivative of f(x) =x² – 6 from limit definition. - Show all steps of working. f(x) :…

A:

Q: The stock price for a certain corporation can be approximated for the years 2007 through 2015 by…

A: At the point of local minima or Maxima the derivative vanishes.

Q: 16. Show that f(x) = Vx - 2 is continuous at x=2 but not differentiable at x=2.

A:

Q: Suppose /has a continuous derivative on the interval [0, 6]. Assume also that f' is increasing on…

A:

Q: Suppose we know that f(x) is continuous and differentiable on the interval [-7,0], that f(-7) = -3…

A:

Q: How must f(0) be determined so that the function f(x) = x2-x ニー x0, is continuous x-1 at X= 0?

A: Let f be a real function . Let a be any point in its domain . If limx→afx exist and equal to fa Then…

Q: Let f be a twice differentiable function on an open interval (a, b). Which statements regarding the…

A:

Q: 3. FIND THE DERIVATIVE BY THE LIMIT PROCESS OFF (x) = Vx + 2.

A:

Q: 9. Is the function defined by gon3 – 3 if 2. continuous at r= 2? differentiable at x = 2?

A:

Q: A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f, the tangent…

A: Given problem:- A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f,…

Q: Consider the function f(x) = -6x² + 8x – 5.f(x) is increasing on the interval (-00, A] and…

A: Find the first derivative of the given function and equate it to zero to find the critical numbers…

Q: Are there independent linear functions with derivative number n – 1 continuous 91 ,..., „,with…

A:

Q: 4. Show that the function is continuous on (-00, 0). f(2) = {0 x* sin(1/x) if x 01 if x = 0 S

A:

Q: 1. Does there exist a differentiable function f that is continuous on the closed interval [1, 4],…

A: Mean Value Theorem (MVT):   If f(x) is continuous on the closed interval [a, b] and differentiable…

Q: 8. Let f(x) = 9x +- Find the critical number(s) and determine whether they are local…

A: fx=9x+1x take the first derivative f'x=ddx9x+1x f'x=ddx9x+ddx1x f'x=9-1x2 take the second derivative…

Q: Find all points with x-values on (0, 2π), where tangent line to the graph of f(x) is horizontal.…

A: Find all points with x-values on (0, 2π), where tangent line to the graph of f(x) is horizontal.…

Q: Sketch the graph of a differentiable function y f(x) through the point (-2,2) if f'(-2)=0 and…

A: Given: To sketch the graph of the differentiable function function y=f(x) through point (-2, 2) if…

Q: let  f(x)=  x+2  if x1 Find the value of k that will make f continuous on (-∞,∞)

A:

Q: Consider the function f(x) = -2x² + 8x – 9. f(x) is increasing on the interval (-o, A] and…

A:

Q: (b) Show that the function defined by √₂²+y f(x, y) = 0 if (x, y) = (0,0) is not differentiable at…

A: On solving this we will get

Q: 4. By the definition of derivative prove that f(x) = √x² +5 is differen- tiable at x=2.

A:

Q: Consider a differentiable function f with domain R and derivatives f'(x)=-aebx(1+bx) and…

A:

Q: 1. Use the first derivative test to find the location of all local extrema for 3 f(x) = -x³ +x+ 18x…

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: The coordinates of the critical point according to the criterion of the first derivative of the…

A:

Q: (b) Use both the first and second derivative tests to show that g(x) = 2tan²x has a relative minimum…

A: The given function is:; g(x)=2tan2x Now differentiate the function with respect to x,…

Q: The critical numbers r = -1 and x = 2 are found from a continuous derivative f(x). Given that the…

A:

Q: The stock price for a certain corporation can be approximated for the years 2012 through 2017 by…

A: Given that                                                         f(x)=6.3x2-168x+1199 derivative…

Q: Find the absolute maximum and minimum values of f(x) = (z² + æ)f over the interval [-3, 4]. and it…

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.