State in your own words the general power rule for differentiating the function h(x)=[f(x)]^n, where n is a real number.

Q: Suppose f(x)=(x−1)/(x+6). Write an expression in terms of x and h that represents the average rate…

A: fx=x-1x+6

Q: Consider the following function. f(x) = −x2 − 6x − 6 Find its average rate of change over the…

A: Solution : According to the question,     The average rate of change of the function f(x) over an…

Q: s rate of change of the function at the given x-value. f(x) = 3x2 + x − 3 at x = 1

A: Given: fx=3x2+x-3 To find rate of change of f(x) at x=1

Q: Find the domain of the function. f(x) = ln ( 1/ (x + 1)

A: f(x)=ln1x+1

Q: Given that f(x) = 3^x and g(x) = ln(x), evaluate both (g ◦f)(2) and (f ◦g)(2). If necessary, round…

A:

Q: Consider the following function, where R is the revenue (in thousands of dollars) and x is the…

A:

Q: Use this formula to find the instantaneous rate of change of the function at the given x-value.f(x)…

A: Given function is

Q: It was determined that the number of prey consumed by a predator over a period of time was a…

A:

Q: Suppose f(x)=6x2+9x−14f. Write an expression in terms of x and h that represents the average rate of…

A: fx=6x2+9x-14

Q: It was determined that the number of prey consumed by a predator over a period of time was a…

A:

Q: Evaluate the function f(x) = log,x at x = 27 without using a calculator. %3D

A: Given that

Q: Suppose f(x) = 15x + 4.5. Write an expression in terms of x and h that represents the average rate…

A:

Q: Suppose f(x)=(x−3)/(x+4) Write an expression in terms of x and h that represents the average rate of…

A: fx=x-3x+4 The average rate of change of f over any interval x, x+h is fx+h-fxh.

Q: Suppose f(x)=6x^3. Write an expression in terms of x and h that represents the average rate of…

A: given, f(x) = 6x3. we have to fing , the average rate of change of f over any interval (x,x+h) and…

Q: In the given question as afollows, sketch the graph of the function and state its domain.   f (x) =…

A: Given, f(x)=3ln(x)

Q: Suppose f(x)=6x2+9x−13. Write an expression in terms of x and h that represents the average rate of…

A: Average rate of change is ratio of change in function values and time interval.

Q: Consider the function f (x) = x³ + 3x + 2. Calculate the average rate of change from x = 1 to x = 3…

A:

Q: Let L(x) be the linearization of the cube root function at x=8. When using L(x) to approximate the…

A:

Q: For what values is the function f(x)= ln(x+1)/x^2+1 continous? Can you please explain how to…

A: If , g(x) is continuous and h(x) is continuous. Then g(x) / h(x) is continuous.where h(x) not equal…

Q: Find the local and absolute extremum for the functions over their domain: 5. f(x) = vx2 + 8x + 20

A:

Q: Consider f(x) = 3X. What is the best approximation for f'(2)?

A:

Q: If L(x)=mx+b is the linearization of the principal square root function of x at x=900, then b= Use…

A:

Q: Suppose f(x)=1xf(x)=1x. Write an expression in terms of xx and hh that represents the average rate…

A:

Q: Find the domain of function defined as follows. y = ln(x + 7)

A: Given       y = ln(x + 7)

Q: Suppose f(x)=(x−4)/(x+4). Write an expression in terms of x and h that represents the average rate…

A: Given: fx=x-4x+4, To find: The expression of average rate of change of f over any interval x,x+h.

Q: Find f’(e) of the following function. f(x)= x3 *(ln x- 1/3)

A:

Q: Find the domain of the function: h(x) = ln x2

A: h(x)=ln x2

Q: Suppose f(x)=2x^3 Write an expression in terms of x and h that represents the average rate of change…

A: Consider the function: fx=2x3 The average rate of change of function over any intervals of length…

Q: 3 Suppose f(x) = 6x°. Write an expression in terms of x and h that represents the average rate of…

A: Given, f(x)=6x3

Q: Find a general formula for f^n. f(x)=7x^2 e^x

A: Consider the given function fx=7x2ex. In order to find the nth derivative f'n, differentiate the…

Q: Find the function whose tangent line has the slope 3x² + 1 for each value of x and whose graph…

A: We have to find the function whose tangent line has the slope 3x2+1 for each value of x and whose…

Q: Suppose f(x)=5x2+8x−16. Write an expression in terms of x and h that represents the average rate of…

A: Average rate of change is ratio of change in value of f(x) and change in x.

Q: Suppose f(x)=6x2+9x−12. Write an expression in terms of x and h that represents the average rate of…

A: The average rate of change is given by: f(x+h)-f(x)h

Q: The population, f, of a small community on the outskirts of a city grew rapidly over a fifteen year…

A: Newton's backward difference formula uses the formula below to approximate f(x) .…

Q: Suppose f(x)=1/x. Write an expression in terms of x and h that represents the average rate of change…

A: given :     f(x) =1xTo compute average rate of change of f over any interval of length h.      f(x)…

Q: Find f' (æ) for f (x) = 7 ln(4 + æ²).

A:

Q: Find the net change in the value of the function between the given inputs.39. f(x) = 3x - 2; from 1…

A:

Q: Find the function whose tangent line has the slope 3x² + 1 for each value of x and whose graph…

A:

Q: Find f''(x) for: f(x)=ln⁡x/4x

A:

Q: Suppose f(x)=x−4/x+1. Write an expression in terms of xx and hh that represents the average rate of…

A: This question can be solved by applying the formula of average change in a closed interval.

Q: If ɛ ER and the function f(x) = ex – 1+ x² is increasing x E R, show also that e >

A: Since f is increasing hence f'(x) >0 for all x

Q: Find the domain of the function. g(x) = ln ( 1/x - 5)

A: given,

Q: Suppose f(x)=5x3f(x)=5x3. Write an expression in terms of xx and hh that represents the average rate…

A:

Q: Suppose we have a revenue function given by R(x)=3x^3−αx, where α is a constant. What would the…

A: Formula used:

Q: Suppose the weight (in pounds) of a baby boy x months old, for his first 10 months can be…

A: Given function, f(x)=1.6x+8.3 Where x is in months.

Q: Find the domain of the function: h(x) = ln(x - 3)2.

A: Given: hx=lnx-32 By using the property of logarithmic function, the given function can be expressed…

Q: Suppose f(x)=x−1x+6. Write an expression in terms of x and h that represents the average rate of…

A:

Q: Find the domain of this function. f(x) = ln(x - 8)

A: We have to find domain

Q: Suppose ƒ is an even function and Evaluate

A: Given f is an even function, ∫-88f(x)dx=18

Q: Consider the following function. f(x) = -x2 - 10x – 9 Find its average rate of change over the…

A: