Transcription of Answers/Solutions to Assigned Even Problems
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Answers/Solutions to Assigned Even Problems
Answers/Solutions to Assigned even ProblemsSection :In Exercises 1-12, compute the derivative of the given function and find the slope ofthe line that is tangent to its graph for the specified value of the independent (x) = 3;x= :Recall that, at this section, we have no shortcut rules for derivatives, andmust use the (limit) definition;f (x) = limh 0f(x+h) f(x)hBut, in this case,fis unusually simple;f(x) = 3. This meansf(anything) = 3In particular,f(x+h) = 3. Hence, we have:f (x) = limh 0f(x+h) f(x)h= limh 0[ 3] [ 3]h= limh 00h= limh 0(0)= 0 Indeed, the graph off(x) = 3 is a horizontal line, so the slope at each point is (x) = 2 7x;x= 1 Solution:You can run through the definition, but again, this function is linear. It sgraph is a line, with slopem= 7. So the slope at each point is 7. In particular,f (x) = (x) =x2 1;x= :Nowfis a curved function. We apply the definition of the derivative:f (x) = limh 0f(x+h) f(x)h= limh 0[(x+h)2 1] [x2 1]h= limh 0[x2+ 2xh+h2 1] [x2 1]h= limh 0x2+ 2xh+h2 1 x2+ 1h= limh 02xh+h2h= limh 0h(2x+h)h= limh 0(2x+h)= 2x+ (0)= 2xThe derivative isf (x) = 2x.
Answers/Solutions to Assigned Even Problems Section 2.1: In Exercises 1-12, compute the derivative of the given function and nd the slope of the line that is tangent to its graph for the speci ed value of the independent variable.
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