1. Which of the following is the linear approximation of the function f ( x )...

1. Which of the following is the linear approximation of the function f ( x ) = 2e^sin (7x) at x = 0?

Group of answer choices

y=cos⁡(7)x+2

y=7x+2

y=14x+2

y=2x+7

y=e^7x+14

2. Recall that Rolle's Theorem begins, ``If f ( x ) is continuous on an interval [ a , b ] and differentiable on (a , b) and ___________, then there exists a number c …'' Find all values x = c that satisfy the conclusion of Rolle's Theorem for the function h ( x ) = x^3 − 7x − 9 on the interval [ − 2 , − 1 ].

3. At x = 1, the function g( x ) = 5x ln(x) − 3/x

is . . .

Group of answer choices

has a critical point and is concave up

decreasing and concave up

decreasing and concave down

increasing and concave up

increasing and concave down

4.If x and y are two real numbers such that 8x − y = 48, what is the smallest possible value of their product xy?

Group of answer choices

−72

−24

−144

Solutions

Expert Solution

milcah answered 1 year ago

Next > < Previous

Related Solutions

Consider the function f(x)=2e2sin(x). In this question, we will first use a linear approximation to estimate...

Consider the function f(x)=2e2sin(x). In this question, we will first use a linear approximation to estimate the value of f(0.1). Then, we will use a Taylor polynomial of degree three to estimate de value of f(0.1). a) What is a good choice for the base point a of the linear approximation and the Taylor polynomial? Answer: a= b) Compute the derivative of f and evaluate it at x=a. Answer: f′(x)= f′(a)= c) The linear approximation L(x) of f(x) based at...

Find the linear approximation of the function f(x,y)= e^(x^2 + 4xy - 2y^2) at (1,2) using the aproximate f(0.99,2.01)

-- Find the linear approximation of the function f(x,y)= e^(x^2 + 4xy - 2y^2) at (1,2) using the aproximate f(0.99,2.01) -- find Zvu for z= f(x,y), x=uv , y= v^2 + u^2 -

Find f(x) if f is a linear function that has given properties. f(-1)=1, f(3)=9 f(x)=

For each of the following, find the linear to linear function f(x) satisfying the given requirements....

For each of the following, find the linear to linear function f(x) satisfying the given requirements. (a) f(0) = 0, f(10) = 15, f(20) = 20 (b) f(0) = 15, f(5) = 6, f(20) = 5 (c) f(10) = 8, f(30) = 12,and the graph of f(x) has y = 20 as its horizontal asymptote

T/F 1) The function f(x) = x1 − x2 + ... + (−1)n+1xn is a linear...

T/F 1) The function f(x) = x1 − x2 + ... + (−1)n+1xn is a linear function, where x = (x1,...,xn). 2) The function f(x1,x2,x3,x4) = (x2,x1,x4,x3) is linear. 3) For a given matrix A and vector b, equation Ax = b always has a solution if A is wide

a. Write the equation of the line that represents the linear approximation to the following function...

a. Write the equation of the line that represents the linear approximation to the following function at the given point a. b. Use the linear approximation to estimate the given quantity. c. compute the percent error in the approximation, 100* (|approximation-exact|)/|exact|, where the exact value is given by a calculator. f(x)=15-3x^2 at a=2; f(1.9)

1.Given the function f(x)=1/x, using 3 rectangles of equal width, find an approximation to the area...

1.Given the function f(x)=1/x, using 3 rectangles of equal width, find an approximation to the area between the curve and the x-axis over the interval [4,8] if the heights of the rectangles are found by evaluating the function at the left endpoints, right endpoints, and midpoints of each subinterval created by a partition of the interval given. 2. Given the function, f(x)=−x3+6x2 using 6 rectangles of equal width, find an approximation to the area between the curve and the x-axis...

Consider a function f(x) which satisfies the following properties: 1. f(x+y)=f(x) * f(y) 2. f(0) does...

Consider a function f(x) which satisfies the following properties: 1. f(x+y)=f(x) * f(y) 2. f(0) does not equal to 0 3. f'(0)=1 Then: a) Show that f(0)=1. (Hint: use the fact that 0+0=0) b) Show that f(x) does not equal to 0 for all x. (Hint: use y= -x with conditions (1) and (2) above.) c) Use the definition of the derivative to show that f'(x)=f(x) for all real numbers x d) let g(x) satisfy properties (1)-(3) above and let...

Consider the following rational function: f(x) = 18 (x-1)/(x^2 - 9) Which of the following are...

Consider the following rational function: f(x) = 18 (x-1)/(x^2 - 9) Which of the following are true? A. The function touches but does not cross the horizontal axis at: x= 1. B. When x is very large and positive, the value of the f(x) approaches to zero. C. The function cuddles up to the vertical lines which pass through x = - 3 and x =3. D. The function cuts the horizontal axis at x = 3 and x =...

Question 1 Let f be a function for which the first derivative is f ' (x)...

Question 1 Let f be a function for which the first derivative is f ' (x) = 2x 2 - 5 / x2 for x > 0, f(1) = 7 and f(5) = 11. Show work for all question. a). Show that f satisfies the hypotheses of the Mean Value Theorem on [1, 5] b)Find the value(s) of c on (1, 5) that satisfyies the conclusion of the Mean Value Theorem. Question 2 Let f(x) = x 3 − 3x...

Subjects