. Find a formal definition for the derivative as we use it in calculus. Then unpack and explain that definition in your own words. Your explanation should connect the limit of the difference quotient, the slope of tangent lines, and the instantaneous rate of change.

5. One of our ideas about Integrals is that they give the âarea under the curveâ. Another idea is that we use an antiderivative in the process to compute an integral. Why are these really the same thing? Iâm NOT looking for you to tell me what the fundamental theorem of calculus is here; mentioning the FTC means EXPLAINING why the FTC works and does what it does. There are other ways to go with this problem, too.

Question

. Find a formal definition for the derivative as we use it in calculus. Then unpack and explain that definition in your own words. Your explanation should connect the limit of the difference quotient, the slope of tangent lines, and the instantaneous rate of change.

5. One of our ideas about Integrals is that they give the âarea under the curveâ. Another idea is that we use an antiderivative in the process to compute an integral. Why are these really the same thing? Iâm NOT looking for you to tell me what the fundamental theorem of calculus is here; mentioning the FTC means EXPLAINING why the FTC works and does what it does. There are other ways to go with this problem, too.

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