Find f'(0), f''(0), and and determine whether f has a local minimum, local maximum, or neither at x = 0. f(x) = (6x +3)² What is f'(0)? f'(0) =| What is f'(0)? f"(0) = Does the function have a local minimum, a local maximum, or neither? O A. The function has a local minimum at x = 0. O B. The function has a local maximum at x = 0. O C. The function has neither a local minimum nor a local maximum at x = 0. Click to select your answer(s).

Q: determine whether the series converges or diverges. If it is convergent, find the sum

A: The given series is in geometric progression so according to geometric series test if common ratio r...

Q: | For what value of a is Sx² – 1, x< 3 |2ax, f(x) = continuous at every x?

A: Let f is continuous at x = 3 then left and right limit are equal.

Q: determine whether the sequence converges or diverges. If it converges, find the limit.

A: We use the ratio test to check convergence.  For that we find a_(n+1) th term 

Q: Find the lengths of the curves 1. The cardioid r = 1 + cos u 2. The curve r = a sin^2 (u/2), 0&lt;= ...

A:

Q: Find the general solution to the given differential equation. (Use C for the constant of integration...

A: Given differential equation

Q: you are standing abore the point 13, 1) ot the surtace 2=10-(2x+242) a) which direction shonld in ve...

A: Given surface

Q: Find f + g, f − g, fg, and  f/g and their domains.  f(x) = 2 − x2,    g(x) = x2 − 9 Find (f + g)(x)....

A: Now, Since (f+g)(x) is a constant function, it is well defined for all real numbers.  Therefore the...

Q: If F(x) = f(xf(xf(x))), where f(1) = 2, f(2) = 3, f '(1) = 3, f '(2) = 4, and f '(3) = 5, find F '(1...

A:

Q: Find the areas of the regions . 1. Inside the oval limaçon r = 4 + 2 cos u 2. Inside the cardioid r ...

A: Replace the variable u with θ The area inside the oval limaçon is given as, Where, a=0 and b=2π A...

Q: Given the function g(t)=(t−1)(t+7)(t−6) its g-intercept is ? its t-intercepts are ?

A:

Q: Evaluate the following integral in which the function f is unspecified. Note that f is the pth power...

A: When x=3 then z=f(3)=6  When x=4 then z=f(4)=7  

Q: Assume that z = ln (ƒ(w)), w = g(x, y), x = sqrt(r - s), and y = r^2s. If gx(2, -9) = -1, gy(2, -9) ...

A: Given Now, we will find partial derivative of w with respect to r and s by using chain rule

Q: Let ƒ be defined on an interval (a, b) and suppose that ƒ(c) ≠ 0 at some c where ƒ is continuous. Sh...

A:

Q: portion=30 /base=228 R= portion/base what is the rate%

A:

Q: Give an informal or intuitive definition of the limit ƒ(x) = L. as lim x--&gt;c Why is the definitio...

A:

Q: Suppose the velocity of an object is given by the following formula: v(t) = 2(t^2) +8t -12 When will...

A: To determine: Velocity of an object is given by the following formula:                              ...

Q: Find the areas of the regions . 1. Inside one loop of the lemniscate r^2 = 4 sin 2u 2. Inside the si...

A:

Q: find an appropriate graphing software viewing window for the given function and use it to display it...

A: Hence the periodicity of the given sine function will be,  The plot looks as shown.  

Q: graph the function ƒ to see whether it appears to have a continuous extension to the origin. If it d...

A: Hi! You have uploaded multiple questions. As per norms, we will be solving only the first question a...

Q: use the formal definition of limit to prove that the function is continuous at c. h(x) = sqrt(2x - 3...

A: To show that the function is continuous at x=2 we will find the left and right-hand limit at x=2. 

Q: Solve: Log(base 4) (x)= 5/2

A:

Q: find a function z = ƒ(x, y) whose partial derivatives are as given, or explain why this is impossibl...

A: We will find f(x,y) from both partial derivatives.  Where g(y) is a function of y and c is integrat...

Q: How do I decide whether this function is maximum or minimum?

A:

Q: What does it mean for a function to be continuous on an interval? Give examples to illustrate the fa...

A: In simple terms, if the graph of a function can be drawn without lifting the pen from the paper, we ...

Q: What is the average rate of change of the function g(t) over the interval from t = a to t = b? How i...

A: The average rate of change of the function g(t) over the interval from t = a to t = b is given by: ...

Q: determine whether the series converges or diverges. If it is convergent, find the sum

A: The given series is 

Q: At what points (x, y, z) in space are the functions continuous?  a. h(x, y, z) = sqrt(4 - x2 - y2 - ...

A:

Q: Find the areas of the regions . 1. Shared by the circles r = 2 cos u and r = 2 sin u 2. Shared by th...

A: 1. Area of the region shared by the circles r = 2 cos u and r = 2 sin u Replace the variable u by θ ...

Q: Differentiate the function. y = tan[In(ax + b)] y' = %3D

A:

Q: Show that each function satisfies a Laplace equation. ƒ(x, y, z) = x2 + y2 - 2z2

A: Again differentiating with respect to x, we get Now partially differentiating given function with r...

Q: Evaluate the limit. (Use symbolic notation and fractions where needed. Enter DNE if the limit does n...

A:

Q: Determine the domain and range of each function. Use various limits to find the asymptotes and the r...

A:

Q: Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the oute...

A:

Q: Consider the equation below. f(x) = e?x + e¬x (a) Find the intervals on which f is increasing. (Ente...

A: Given

Q: How long will it take a $600 investment to be worth $700 if it is continuously compounded at 11% per...

A: Write the continuous compound interest formula,

Q: How do I find the derivative of this problem?

A:

Q: Use graphing software to graph the function. Select a viewing window that reveals the key features o...

A: We first graph the equation x2 + 2x = 4 + 4y - y2 in [-10,10]x[-10,10] viewing window to determine w...

Q: Is there any reason to believe that there is always a pair of antipodal (diametrically opposite) poi...

A:

Q: Evaluate the limit. (Use symbolic notation and fractions where needed. Use the symbol oo for infinit...

A:

Q: Is there a direction u in which the rate of change of ƒ(x, y) = x2 - 3xy + 4y2 at P(1, 2) equals 14?...

A:

Q: determine whether the series converges or diverges. If it is convergent, find the sum

A: We will apply the ratio test to figure out if the series is convergent or not. Let's take the ratio ...

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

A:  

Q: On what intervals are the following functions continuous? a. ƒ(x) = tan x b. g(x) = csc x

A: a) a) We write f(x) as rational function The denominator can not be equal to 0. where n is an inte...

Q: Find the absolute maxima and minima for  f(x)  on the interval  [a, b]. f(x) = x3 + x2 − x + 8,    ...

A:

Q: For problems 2-3, find the first 6 partial sums for the series; does it appear to converge? If so, f...

A: As a first step let's assign the values of 1 to 6 to evaluate the first six terms of the series. Ter...

Q: Find all possible oblique asymptotes . y = sqrt(x2)+1

A:

Q: verify that wxy = wyx . w = x sin y + y sin x + xy

A:

Q: find the values of the derivatives ds/dt at t=0 if s = 2/(4 - t)

A: Given function is Differentiating with respect to t, we get

Q: Let w = x^2e^2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y...

A: Given  By chain rule of differentiation , we have