f '(x) does not exist. (c) O xo O X1 O x2 O X3 O X4 O none of these f has a relative maximum. (d) O xo O X1 O x2 O X3 O X4 O none of these (e) f has a point of inflection. O xo O X1 O x2 O X3 O X4 O none of these

Q: Find the local maximum of f(x) = -sin2x – x defined on 2'2

A:

Q: Find the critical points of the function f(x) = x³ + 1¹5 x² + 50x + 8. Use the First Derivative Test…

A:

Q: 4) Find the critical points of the function f(x) = x²- 9 x* + 15x +3 and identify their nature. Draw…

A: Given that: f(x)=x3-9x2+15x+3 The graph is shown below

Q: 2. Let g(x) = x – 3x 3 . (a) points of g(x). Determine the critical Use the Second Derivative (b)…

A: To find- critical points, local extrema and inflection points of g(x).

Q: 8. A limit exists if both the right-hand and left-hand limits are equal. 9. The acceleration…

A: Given :   Limit rule, acceleration, quotient rule

Q: Let f(x)=x+(1−x)^(1/2) Find the local maximum and minimum values of f using both the first and…

A: For local maxima or minima:The first derivative test is f'(x) = 0The second derivative test…

Q: The derivative of the function f(x) = 25 x3 -6 x2 +7x- 88 at X = 3 using a step size of 0.5 and…

A: on solving we get

Q: Prove that Pr (|X − a| < τ ) takes its maximum value when a = µ where X ~ N (µ, σ2)

A:

Q: Find f'(x). f(x) = O O O 6x - sin² (5x) f'(x) = O f'(x) = f'(x) = f'(x) = = 6-10sin(5x)cos(5x) 2√6x…

A:

Q: Let f(x)=x+(1-x)^(1/2). Find the local maximum and minimum values of f using both the first and…

A:

Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(x - 1) + 2* -x has a critical number…

A:

Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

A:

Q: Find the absulote maximum of x40-x20 on the interval [0,1],also find its absolute maximum value

A:

Q: At what x-value is the global minimum for f(x)=x2−4x+3 within the interval  0≤x≤5?

A:

Q: 3. Iff has a local maximum at x – 1, then what can you say about f'(1)? What if you also know that f…

A: Given: The function fx has a local maximum at x=1. First derivative test: Let f be differentiable…

Q: Let f be a continuous function with f'(x) = 3x² Of has no relative maxima. 0x=0 0x=2 0x=1 - 6x. At…

A: f be a continuous function with f'x=3x2-6x

Q: Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 2 at x = −2 and a…

A:

Q: Give an example that: the function f has a local maximum at x = 1/2, but it is not differen- tiable…

A: Consider the function:

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

A: Here we will apply first derivative and equate it to 0 to get the critical points and then apply…

Q: Consider the following function f(x)=2(x+1)2 in the interval [-2, 3] The critical point(s) =…

A: For critical points put f'(x)=0.

Q: 2 The function defined by f(x)= x-3x for all real numbers x has a relative maximum at x = %3D

A:

Q: b- find any locl maximum and locl minimum values by using first derivative: f(x)=x-2x²

A: We can use application of derivative order to solve the given problem.

Q: 4. If f has a local minimum at x = 0 and a local maximum at x – 2, what can you say about f'(0) and…

A: f has a local minimum at x=0 and a local maximum at x=2.

Q: Consider the function f(x) = z over the interval (-2, 2). Does the extreme value theorem guarantee…

A:

Q: Find local maximum or local minimum of f(x) = - sin 2x -x defined on 2'2

A:

Q: Let f(x) = e^(2−x^2). Find the x-coordinates of all critical points of the f. Determine whether each…

A:

Q: 3. The function f(x) = x^4 − 4x^3 + 8x has a critical point at x = 1.(a)  Find f"(x).   (b) Then use…

A:

Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

A:

Q: (5) Use the first derivative test to classify the critical numbers of the function s(r) = 2¹-4r³+17.…

A:

Q: A function f has derivative f′(x)=x^3(x−1)^2(x+1)(x−2). At what numbers x, if any, does f have a…

A:

Q: Find the local maximum value of f using both the First and Second Derivative Tests. f(x) = x + V1 -…

A: First calculate critical point at which either local maxima or local minima will occur by putting…

Q: Q2: Find all critical numbers of the function f(x) = (x- 2)2/3 +1 and classify each critical point…

A: Here we will find out the required value.

Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

A: Differentiate the given function with respect to x and equate it to zero,…

Q: b- find any locl maximum and locl minimum values by using first derivative: f(x)=x*-2x²

A: Points of local extremum can be calculated by using the first derivative. These are points which…

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: If f has a local minimum at x = 0 and a local maximum at x = 2, what can you say about f'(0) and…

A:

Q: Find the maximum value of f(x)=2sin(x)cos(x).

A: Given: f(x)=2sinxcosx The above function can be written as: f(x)=sin2x…

Q: Find local maximum or local minimum of f (x)=sin 2x-x defined on 2 2

A: The given function is fx=sin 2x-x. Obtain the critical points as follows. Find f'x as…

Q: On the graph of f(x)=sinx and the interval [−2π,0), for what value of x does f(x) achieve a minimum?

A: The given function is fx=sinx Differentiating w.r.t. x to both sides- f'x=cosx To find the critical…

Q: Find the absolute maximum and minimum vaules of the funct ion g(x)= (x^2-3x+4)/(x-1) on the interval…

A:

Q: 1. Id f (u) = - sec u, find f '(u)

A: According to our guideline, we are supposed to install only the first question if you want any…

Q: (1) Find the derivative of the function f(x) = 2x³ - 12x² +4 and use it to find the critical numbers…

A: Solution is given below:

Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

A:

Q: What values of a and b make ƒ(x) = x3 + ax2 + bx have a local maximum at x = -1 and a local minimum…

A: Given: fx=x3+ax2+bx To find a, b such that function has local maxima at x = -1 and local minima x =…

Q: (2x - 2 x² - x f(x) = x² 4 graphing calcu x 2 x = 2

A:

Q: Where are there local minimum(s)/maximum(s) f(x)=3(2x-1) -4(x+1)?

A:

Q: What is the x-coordinate of the global minimum of the function f(x) = x – 3 ln x – 2 for the…

A: