x - 4 x<0, is one-to-one. The function f(x) = 2x2 (a) Find its inverse and check your answer. (b) Find the domain and the range of f and f' (a)f (x) = (Simplify your answer.) %3D

Q: finding the local mins and maximums and the intervals of increase and decrease and making a sign…

A:

Q: (a) Find the equation of the tangent line to the graph of the function f(x) = 3x² at the point (-2,…

A: (a)   Differentiate the function with respect to x is,   Substitute -2 for x in the above equation.

Q: inverse of the function x= 2/ y-3

A: Given:

Q: (a) find an equation of the tangent line to the graph of f at the given point, (b) use a graphing…

A: Explanation: Given that,  f(x)=x2+3point (-1,4)   Concept Used: First derivative of the given…

Q: (a) find an equation of the tangent line to the graph of f at the given point, (b) use a graphing…

A: given: fx=x3+4x-1x-2point 1,-4

Q: (a) find an equation of the tangent line to the graph of the function at the given point, (b) use a…

A: To find the equation of tangent, first find the slope by differentiating the function f(x)=12xlnx2…

Q: erentiate the following function. You do not need to simplify the derivative. - 12x e f(x) x3

A:

Q: Express y as a function of x.The constant C is a positive number. ln y = 2 ln x - ln(x + 1)+ ln C

A:

Q: can you show me how I would find the domain of the derivative? What’s the difference between the…

A: We need to find Domain of derivative.

Q: Find the derivative of the function. (Simplify your answer completely.) f(x) = e* In x + 7 f'(x) =…

A:

Q: (a) Use the Second Derivative Test to find the local extreme values of the function f(x) = (x³ +…

A: Note:- These are multiple questions and according to our company guideline we can do maximum one…

Q: The graph of a function f is given below. According to the graph, the derivative of the function…

A: we have given the graph of the function f, it has local minima at x=2 (as it has minimum value in…

Q: (a) find an equation of the tangent line to the graph of f at the given point, (b) use a graphing…

A: Given: fx=x-2x2+4.

Q: The rabbit population in a national park rises and falls throughout the year. The population is at…

A: Given:         Function f(x) =5000sinπ6x-π2+11,000         where x is the time in months and f(x) is…

Q: determind the derivative of a function Let f(x) = In (x^2+16x+73) f'(x)=

A:

Q: Express y as a function of x. The constant C is a positive number.; ln y = 2 ln x - ln(x + 1) + ln C

A: To express y as a function of x: lny=2lnx-ln(x+1)+lnC Solution: Given equation is:…

Q: (a) find an equation of the tangent line to the graph of the function at the given point, (b) use a…

A: To find the slope of the line, differentiate f(x) with respect to x, using the product rule,…

Q: Express y as a function of x. The constant C is a positive number.; ln(y - 3) = - 4x + ln C

A: One property of logarithm that will be used is eln x=x. One property of exponentials that will be…

Q: (a) find an equation of the tangent line to the graph of f at the given point, (b) use a graphing…

A: Given, fx=x2+2x-1; (1,2)

Q: Find a function f that has the derivative f '(x) and whose graph passes through the given point. f…

A: Solution: The objective is to find the function f(x)

Q: The graph of a function f is given below. According to the graph, the derivative of the function…

A:

Q: (a) Use the Second Derivative Test to find the local extreme values of the function f(x) = (x³ +…

A:

Q: (a) find an equation of the tangent line to the graph of f at the given point, (b) use a graphing…

A: f(x)=x, (1,1)

Q: (a) find an equation of the tangent line to the graph of f at the given point, (b) use a graphing…

A: The given equation of curve is f(x)=x+3x-3 ,  (4,7) (a) find an equation of the tangent line to the…

Q: 6) a) State the definition of f'(x), the derivative of a function f at value x. b) Use the…

A: We have to solve

Q: f(x)=sinx - x/2, find the local Maxima and minima of the function

A: We first find the critical point by solving f'(x)=0

Q: Express y as a function of x.The constant C is a positive number. ln(y - 3)=4x + ln C

A: Given, ln(y - 3)=4x + ln C

Q: Let f (x) = x* + x³ + x² + x. It is difficult and extremely ugly to find a formula for f-1(x).…

A: We will use the relation between f and f-1 for this problem.…

Q: ax + b (x – 1)(x – 4) at point (2, – 1), determine the values of a and b. If the graph of the…

A: Given: g(x)=y=ax+b(x-1)(x-4) Since, the point (2,-1) is lying on the given curve. So, when x=2,y=-1.…

Q: x2 -4 b) By use derivative sketch the function f(x) %3D 2x

A:

Q: The graph of a function f is given below. According to the graph, the derivative of the function…

A: When x tends to 2- then the sign of derivative is negative since it is decreasing from left side of…

Q: Define f(x)=2x^4-3x^2 as a Maple function. Find the equation of the tangent line at the point x=2.3.…

A: We have,  fx=2x4-3x2 The derivative of fx is f'x=8x3-6x Slope of tangent line at (2,3) is f'2=8…

Q: Find a function f that has the derivative f (x) and whose graph passes through the given point. f…

A:

Q: Find the first and second derivatives of the function. (Factor your answer completely.) f(x) = (4x2…

A:

Q: y = (x + 2)

A:

Q: %3D The function f is defined by the cquation above for all positive real numbers x. What is the…

A:

Q: 3 If f(2) - 8, and f'(2) 4 - 1 Let f'(x) be the inverse function of f(x). (f-1)'( - 8) = - 1 Write…

A:

Q: Example 2: For the function below, find any local extrema using the Second Derivative Test. Then…

A: Find the maximum and minimum of the function using second derivative test

Q: Find the first and second derivatives of the function. (Simplify your answer completely.) 9. f(x) =…

A:

Q: Instructions: solves inverse function with t's domain and range 1. f(x)= (x-3)2 +7 2. f(x)=3-(x-5)2…

A: Given: 4.f(x)=x2+2x-2

Q: given function. f(x) = (2x+3x-)(2x³-3x-) a. -444 Find the first derivative (f/(x)) of f(x). b.…

A: We can find the derivatives of given problem.

Q: fihd the deriVatives of the functions. (a) f)=メ+ 5x +

A:

Q: A function is given. f(x) = x³ - 9x; x = 0, x = 10 (a) Determine the net change between the given…

A: A detailed solution is given below

Q: f(x), a. find the slope of the tangent line to its inverse function f-1 at the indicated For the…

A: a)The slope of  y=f-1x is     y'=1f'f-1x given fx=2-3+x2f'x=2×-1x2-32×2x       =-4xx2-32

Q: x² -1 Example: Let f(x): x' +1 %3D What is the domain? Determine the sign of the function as x…

A:

Q: All QUESTION 1 Find the derivative of f(x) = 6x Do not include "f'(x) =" in your answer. For…

A: Identity to be used - ddxxn = nxn-1

Q: Find the first and second derivatives of the function. g(x) = −7x3 + 21x2 + 5x − 64

A: Given function gx=-7x3+21x2+5x-64

Q: x2-3 b) By use derivative sketch the function f(x) x-2

A:

Q: Compute f'(x). f(x)= 8x^-3    ,  a=5   f'(x)=____________ Find an equation of the tangent line…

A: We have: f(x) = 8x-3 We need to calculate the value of f'(x) using the formula: xn = nxn-1  Thus,…

Q: (c) Find an expression for the second derivative of 1/g(x) in terms of g, g', and g", explaining…

A: