Chain Rule Describe the Chain Rule for the composition of two differentiable functions in your own words.

Q: True or false: y = ±√(x2 - 1) defines y as a function of x._______

A: All function which have y = f(x) form are defined as a function of x.

Q: A rectangular box has a square base. Its height is half the width of the base.Find a function that…

A: Let the length of the box= w So the width=length = w (because square base) So, height = w/2

Q: nly ENRICHMENT ACTIVITY 1 Direction: Determine the value of function and its inverse. Then draw the…

A: Step:-1 Given function is  fx=2 x +1    x= -2 then, put x= -2 in f(x), we get fx=2 x +1f-2=2 -2…

Q: -9, f' (-1) = 0, 6. f (–1) = – f (2) = -1, f' (2) = 3, f (5) = 4, f' (5) -1

A: Here is the solution of the given problem. Rough sketch of a function

Q: True or false. If true, explain why. If false, explain why or give a counter example: If f and g are…

A:

Q: UESTION 4 Write the function in slope-intercept form whose graph satisfies the given conditions.…

A:

Q: Analyze the function f (x) -x + 18 if x 10

A:

Q: Utility is a type of function that occurs in economics. When a consumer receives x units of a…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: closed aluminum can of volume is to be in the form of a right-circular cylinder. Find a mathematical…

A: A closed aluminum can of volume is to be in the form of a right-circular cylinder. Find a…

Q: Activity 2: Let us try to find where a function is increasing or decreasing given the following. 1.…

A:

Q: q.no Use a graphing utility to graph the two functions f (x) = x2 + 1 and g(x) = lxl + 1 in the same…

A: Here we have to graph the two functions,  f(x)=x2+1 ........(1)g(x)=|x|+1...........(2)

Q: Continuity and Differentiability Describe the relationship between continuity and differentiability.

A: Difference between Differentiability and continuity: We know that a function is differentiable if it…

Q: example to prove 2. Show that a constant function is continuous. Present an the proof.

A:

Q: What is the rule for calculating the derivative of the composition of two differentiable functions?…

A: We have to explain how to calculate derivatives of composite function.

Q: III. DIRECTION: Determine the composite of two functions. (2points each) f(x) = x + 3, g(x)= 2x² - 9…

A: Given fx=x+3, gx=2x2-9 and hx=x2.  1) fx+gx=x+3+2x2-9fx+gx=2x2+x-6    2) fx·h(x)=x+3x2fx·h(x)=x3+3x2…

Q: Find differentiable functions f and g that satisfy the specified condition such that xlim5 f(x) = 0…

A: Given: f(x) and g(x) which is differentiable and satisfy  limx→5 f(x)=0   and  limx→5 g(x)=0

Q: True or false: y = x2 - 1 defines y as a function of x._______

A:

Q: Explicit and Implicit Functions Describe the difference between the explicit form of a function and…

A: Explicit Functions : When in a function the dependent variable is explicitly isolated on either…

Q: The sand in an hour glass drops at a constant rate of 2.5 cubic millimeters every second. The amount…

A:

Q: Graph analysis of Piece-wise function (Use proper mathematical notation). j. Intevals of x for…

A: (j) The graph is increasing when slope is positive or f'(x) > 0 and the graph is negative or…

Q: Sketching a Graph Sketch the graph of a differentiable function f such that f(2) = 0, f' 0 for 2 <…

A: Given: x∈-∞,2

Q: ACTIVITY 1: CONTINUITY AND DIFFERENTIABILITY Direction: Apply the concepts that you have learned…

A:

Q: Question No: 5 Taking three different examples, justify that every continuous function is not…

A: Continuous function: A function is said to be continuous function if both left hand limit and right…

Q: function f(x) is defined below. What is the end behavior of f (x)? f(x) = -9x + 432x – 1152 %3D as x…

A:

Q: )  a definition of a Piecewise Function 2)  how to evaluate a piecewise defined function

A:

Q: y = 2x – 5 on interval ( - 0, 0)

A:

Q: - f(x) = |x² – 9| 12 10+ 2 -4 -2 2 4

A: we have f(x)=x2-9Now check the differentiability of the function.put x2-9=0⇒x2=9⇒x=±3

Q: 2. Find traits and sketch the graph the equation for a function g (æ) that reflects the function f…

A: Note that, to reflect a function fx over the x axis, find -fx. Here, the given function is…

Q: Describe the x-values at which the function is differentiable. (Enter your answer using interval…

A: We need to find the x-values at which the given function is differentiable. We are given the…

Q: Let f(x) = x² – arcsin(x). • What is the domain of the function f? Explain. • Find and classify all…

A: The solution of the problem is given in the next steps.

Q: The regular price of a pair of jeans is x dollars. Let f(x) = x - 5 and g(x) = 0.6x. a. Describe…

A: The regular price of a pair of jeans is x dollars. Let f(x) = x - 5 and g(x) = 0.6x.a. Describe what…

Q: f(x) = x³-4x, for x in the interval [-1,2]

A: To find the function is increasing or decreasing in the given interval

Q: Describe all functions y=f(x) which are defined for all x∈R and satisfy the equation f(x)= 1/f(x)

A:

Q: Let f(x) = x2 − arcsin(x). What is the domain of the function f? Explain. Find and classify all…

A: For the solution follow the next steps.

Q: Quotient of two functions: Basic

A: Answer and explanation is given below...

Q: Increasing and Decreasing Functions Describe the Test for Increasing and Decreasing Functions in…

A: Given: Increasing function and decreasing function:

Q: Describe the transformation in this function: f (x) = 2|x|

A: In order to check the transformation in any function, we compare it with its parent function for any…

Q: Determining Whether an Equation Is a FunctionDetermine whether the equation x2 + y2 = 1 defines y as…

A: Given that, x2+y2=1

Q: Find and classify all points where f'(x) = 0. Find and classify all points of inflection. Find…

A:

Q: How do you find the composition of functions?Please include an example with your explanation.

A: If there are two functions and then substituting one function into another function is said to be…

Q: Linear function or Not a function

A:

Q: Function Q: Function R: y= 3x-2 Determine whether each value is greater for function Q, the same for…

A: Rate of change = dydx

Q: Determining Whether an Equation Is a FunctionDetermine whether the equation y = 2x - 5 defines y as…

A: To determine whether the equation y=2x-5 defined y as a function of x. Solution: We know that a…

Q: Vertical Line Test for Functions InExercises 11–14, use the Vertical Line Test todetermine whether…

A: '' Since you have asked a question with multiple subparts, we will solve first  three sub-parts for…

Q: "5. f(x) : х — 3 2 4 2. 2.

A:

Q: Determine if the following piecewise function is differentiable at its origin.

A: We want to find whether the given piecewise function is differentiable at the origin or not. To…

Q: determine the homogeneity of the functions. If it is homogenous, state the degree the function.

A:

Q: Partial derivatives graphically is define as ) The derivative of the whole thing O The 2D slope of…

A: Partial derivative represents the 2D slope of the slice of a 3d graph

Q: cotx s the function F(x)3D even or odd or not.

A: Here we have to determine the given function is even or odd or not. We have, F(x)=cotxx2

Q: if true: explain why the statement is true for all cases • if false: disprove with a counterexample.…

A: A critical number is a point on a function curve where the derivative equals zero or the function is…