Consider the graph: Using the graph and intervals noted, explain how a function being increasing or decreasing relates to the first derivative.

Q: -53-2 23 45 -3 -5 Write an equation for the function graphed above

A: Shifting of graph properties: If we have given graph of y = f(x) and c be any positive constant then…

Q: y is a variable that takes values that change with time, and the relationship between them is it has…

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Q: Make a function that violates Clairault's Theorem. Explain why it does. Show how you got it.

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Q: Give 5 examples of Transforming a Unit Function Graph to Algebraic Equation

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Q: Each graph represents f"(x) (not the original function) 6. Find the x-coordinates of all inflection…

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Q: 3. Using the function below, answer the questions to the right. Identify the parent function: Even…

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Q: Exercise refer to the function

A: To Find :                   What happens when x approaches 1 from LHS and RHS

Q: When is a function described in pieces?Give an example?

A: A function is said to be piecewise if it is defined using more than one formula where each formula…

Q: Explain Increasing and Decreasing Functions?

A: Increasing Function: Let y = f(x, y) be differential function on (a, b). If for any two points x1,…

Q: Determine the equation of the function depicted by the following graph.

A: Given data:     The given first point is: (x1,y1)=(-4,0). The given second point is:…

Q: The boxes that are checked correspond to functions that are: Increasing Decreasing

A: We need to provide boxes that are checked when a funtion is increaing and decrasing.

Q: Can you please help me out?

A: Given data points

Q: Briefly explain what the Mean Value Theorem tells us. Why do we require that f be a continuous…

A: Explanation given below...

Q: Let e be a positive number. Explain how to shift the graph of y = f(x) upward, downward, left, or…

A: Given: y=f(x)'c'  be the positive real numberTo shift the graph of y=f(x),  upward, downward,left,…

Q: Example 4: Evaluate the difference quotient for the given function. Simplify your answer.…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: