Consider the function f(x)= 7 - 7x^2/3 defined on the interval [-1, 1]. State which of...

Consider the function f(x)= 7 - 7x^2/3 defined on the interval [-1, 1]. State which of the three hypotheses of Rolle’s Theorem fail(s) for f(x) on the given interval.

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milcah answered 2 years ago

Consider the graph defined by f(x) = (x-3)2 a) state the coordinates of the vertex and...

Consider the graph defined by f(x) = (x-3)2 a) state the coordinates of the vertex and the direction of opening of f(x) b) Find the maximum and minimum values of f(x) on the interval 3<=x<=6 c) Explain how you could find part b) without finding the derivative

1. (8pt) Consider the function f(x) = (x + 3)(x + 5)^2 √ (7 − x)...

1. (8pt) Consider the function f(x) = (x + 3)(x + 5)^2 √ (7 − x) whose first and second derivatives are f'(x) = ((x + 5)(139 + 12x − 7x^2))/2 √ (7 − x) , f''(x) = (35x^3 − 225x^2 − 843x + 3481)/ 4(7 − x)^3/2 . Note: 35x 3 − 225x 2 − 843x + 3481 has three roots: x1 ≈ 7.8835, x2 ≈ −4.3531 and x3 ≈ 2.8982. (a) (1pt) What is the domain of f(x)?...

For the function f(x) = x^2 +3x / 2x^2 + 7x +3 find the following, and...

For the function f(x) = x^2 +3x / 2x^2 + 7x +3 find the following, and use it to graph the function. Find: a)(2pts) Domain b)(2pts) Intercepts c)(2pts) Symmetry d) (2pts) Asymptotes e)(4pts) Intervals of Increase or decrease f) (2pts) Local maximum and local minimum values g)(4pts) Concavity and Points of inflection and h)(2pts) Sketch the curve

Using Matlab, consider the function f(x) = x^3 – 2x + 4 on the interval [-2,...

Using Matlab, consider the function f(x) = x^3 – 2x + 4 on the interval [-2, 2] with h = 0.25. Write the MATLAB function file to find the first derivatives in the entire interval by all three methods i.e., forward, backward, and centered finite difference approximations. Could you please add the copiable Matlab code and the associated screenshots? Thank you!

Expand the function, f(x) = x, defined over the interval 0 <x <2, in terms of:...

Expand the function, f(x) = x, defined over the interval 0 <x <2, in terms of: A Fourier sine series, using an odd extension of f(x) and A Fourier cosine series, using an even extension of f(x)

Consider the following function: f(x) = -5x3 + 180x2 – 7x – 50

Consider the following function: f(x) = -5x3 + 180x2 – 7x – 50 a.) Solve for the “inflection point” of this function ( show your work). b.) Solve for f ''(5) ( i.e., find the second derivative for the function if x = 5 ; show your work). c.) Is x = 5 in the concave region of the graph of this function OR in the convex region of the graph of this function ( i.e., choose “ concave” or “convex”)? Briefly explain how your answer to b.) is...

A. In the following parts, consider the function f(x) =1/3x^3+3/2x^2−4x+ 7 (a)Find the intervals on which...

A. In the following parts, consider the function f(x) =1/3x^3+3/2x^2−4x+ 7 (a)Find the intervals on which f is increasing/decreasing and identify any local extrema. (b) Find the intervals on which f is concave up/down and find any inflection points. B. Consider the function f(x) = sin(x) + cos(x). Find the absolute minimum and absolute maximum on the interval [−π,π].

Consider a distribution with the density function f(x) = x^2/3 for −1 ≤ x ≤ 2....

Consider a distribution with the density function f(x) = x^2/3 for −1 ≤ x ≤ 2. (a) Randomly pick a sample of size 20 from this distribution, find the probability that there are 2 to 4 (inclusive) of these taking negative values. (b) Randomly pick an observation X from this distribution, find the probability that it is between 1.2 and 1.4, i.e., P (1.2 < X < 1.4). (c) Randomly pick a sample of size 40 from this distribution, and...

On the interval [-1,1], consider interpolating Runge’s function f(x) = 1/ (1 + 25x^2) By Pn(x),...

On the interval [-1,1], consider interpolating Runge’s function f(x) = 1/ (1 + 25x^2) By Pn(x), use computer to graph: (c) Take 11 equally spaced nodes in [-1,1], starting at –1, ending at 1, and obtain the interpolating polynomial P10(x). Also, use 11 Chebyshev nodes in [-1,1] and obtain Pc(x), the corresponding interpolating polynomial. In the same graph, plot the three functions f(x), P10(x) and Pc(x) over the interval [-1,1] . Use different line-styles, so that f(x), P10(x) and Pc(x)...

The function F(x) = x2 - cos(π x) is defined on the interval 0 ≤ x...

The function F(x) = x2 - cos(π x) is defined on the interval 0 ≤ x ≤ 1 radians. Explain how the Intermediate Value Theorem shows that F(x) = 0 has a solution on the interval 0 < x < .

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