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

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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: 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: 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: 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: