8. Find all the points in the interval [1,5] for f(x) = -x² + 6x – 6 such that the function verifies the Rolle's theorem

Q: B) Estimate the next root of the function f(x)=x^3-x-1 using Muller method, let x0=1, x1=2, x2=1.5

A: Muller method: The Muller approach is applicable to any root-finding programme, but it is especially…

Q: 5. Show that the function h(x, y) defined by if r2 + y? 1 is discontinuous.

A:

Q: Verify that the three conditions of the hypothesis of Rolle's Theorem hold for the function f (x) =…

A: 1. f(x) is continuous on the closed interval [a,b] 2. f(x) is differentiable on the open interval…

Q: Verify the Rolle's Theorem for the function (x2-1)(x-2) on [-1,2] find the point in the interval…

A: Given function is : fx=x2-1x-2 To verify the Rolle's Theorem and find the point in the interval…

Q: e^x=3-2x

A: Given; ex=3-2x,(0,1)

Q: Prove, without graphing, that the graph of the function has at least two x-intercepts in the…

A: Given   y = sin (x3) ....(1)   , (1, 2)

Q: 25. For the function f(x) = 45x3 - 3x5, determine the interval(s) for which f(x) decreases. O (3, 3)…

A: We will solve this question by  differentiating f(x) and then finding the intervals for which the…

Q: 5. Show that the function h(r, y) defined by if + y 1 is discontinuous.

A:

Q: If we apply Rolle's Theorem to the function f(x) = 2x² – 16x – 5 on the interval [2, 6], how many…

A: Given,          fx=2x2-16x-5 on the interval 2,6.We know that,         Rolle's theorem states that…

Q: Q1: If the function f(x) define as f: R→ R such that f(x) = (x+1, x>2 x²-1, x≤2 Show that the…

A: This is the question to check the differentiability of the function.

Q: 21 (d) Suppose that f(1) = 0. In the xy-plane provided, draw a sketch that show of the graph of the…

A:

Q: Verify the Rolle's theorem for the function (x² – 1)(x – 2) on [-1,2] Find the point in the interval…

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

Q: Consider the function f(x)=3x2−4x+10,  0≤x≤8f(x)=3x2-4x+10,  0≤x≤8. Use the derivatives to…

A:

Q: Consider the piecewise function: |x- 1| x² – 1' x <1 f(x) = (Ax² + 6, x 2 1 For what real number A…

A:

Q: Show that f is not differentiable at x = 1 and has a corner in its graph there. x 1

A:

Q: Verify the Rolle's Theorem for the function (x2 – 1)(x – 2) on [-1,2] find the point in the interval…

A:

Q: Find all the points in the interval [1, 5] for f (x) x + 6x – 6 such that the function verifies the…

A:

Q: Determine the c which satisfy the conclusion of Rolle’s Theorem for the given function and interval.…

A:

Q: 1. Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A: see 2nd step

Q: Show that the given function is analytic in an appropriate domain. 2- y S(x) = Tr+2}* +3y² (x+2)*…

A: Please consider the handwritten solution.

Q: Suppose that a function h satisfies −x^2 ≤ h(x) ≤ x^2 for all x. Prove that h is differentiable at x…

A:

Q: The graph of f(x)= x2 - 1 is concave down on interval | (-1,1) ^O (0,1) BO (-1,0) U (1, ∞ )co (- 00…

A: From the given problem:   fx=xx2-1   As we know that for concave downward:   f''x&lt;0   So,…

Q: 14. Consider the function f (x) = x²e+x . f(x) has two inflection points at x = _ and x =_.

A:

Q: 19.D. Show that the function defined by g(x) g² sin (1/x), x * 0, %3D = 0, 0, is differentiable for…

A:

Q: (11) (C) For the function f(x) = x° – x, determine whether the hypothesis of Rolle's theorem hold on…

A:

Q: of of and ду For the function f(x,y) = In (7x + 9y), find

A: The given function,     f(x,y)=ln7x+9y

Q: 4. At what value(s) of x is the function x + 2 x2 for x 1 f(x) = 3- x discontinuous?

A:

Q: Prove that f(x) = other than the graphing method. x² – 1 is continuous at c = 0 by any method |

A:

Q: 5. Show that the function h(x, y) defined by 1 if a? + y? 1 is discontinuous.

A: We can solve this using R.H.L ≠ R.H.L

Q: Find the absolute maximum and absolute minimum of f(z) = +z - 48z over the interval (4, 8).

A: We have to find the absolute maximum and absolute minimum for the function f(x)=x33+x2-48x over the…

Q: Suppose f and g are differentiable functions on R such that, (x²+1)f (x) + 3xf(x) = e*2 + 7x and…

A:

Q: Suppose that f (0) = 2 and f' (x) ≤ 3 for x &gt; 0. Apply the MVT to the interval [0, 4] to prove…

A:

Q: Use the Extreme Value Theorem to show that each of the following functions has a positive maximum on…

A:

Q: The graph of f(x)= x2 -1 is concave up on interval (-1,1)^O (0,1) 0 (-1,0) U (1, 0 )co…

A: Given,  The function fx = xx2-1  We have to find the interval in which the graph of  fx = xx2-1 is…

Q: Find the values of k in f(x)=x^2-kx such that the line y=5x-4 is tangent to the function.

A:

Q: if x1 O No, since g(x) is undefined at x=1. O Yes, and g'(1)=3. O Yes, and g'(1)=8. O No, since g(x)…

A: Given

Q: 2. Consider the function f with domain (-2, 0): 3|22 – 1| if – 2<r<1 2.r2 + 2x – 4 f(x) = 3 if r = 1…

A:

Q: Suppose h(x) = [,f(t)dt on the interval [0, 12], where f (t) is shown in the graph below. f (t) -4-…

A:

Q: Find m so that f(x) is continuous at x = 2. x +4 if x 2 -

A:

Q: Use the intermediate value theorem to show that f(x) = (e^−x^2)−x has at least one root in the…

A:

Q: Use the intermediate value theorem to show that f(x) = e −x 2 − x has at least one root in the…

A:

Q: Find the interval(s) on which f(x) = 2x^3-3x^2-12x+1 is concave up.

A: Given : fx = 2x3 - 3x2 - 12x + 1

Q: Use the Intermediate Value Theorem to show there is a root of the given equation in the specified…

A: Intermediate value theorem states that if “f” be a continuous function over a closed interval [a, b]…

Q: Q.4 A/ Prove the function continuous at x = -2, (x2 + 5 13-3x where %3D if x<-2 if x 2-2 f(x) = %3D

A:

Q: Let f(x, y) = -e2"-y + In(3x – y). Find the domain of this function.

A:

Q: Show that there exists an x in the interval (0, 1) that satisfies the given equation V = 1-x Hint:…

A:

Q: Verify Rolle's theorem for f(x) = x² - 9x +6 over the interval [0, 3].

A: