Question: Use the function below to answer parts (a)-(c). f left parenthesis x right parenthesis equals StartFraction 1 Over x EndFraction (a) Use the formal definition

Use the function below to answer parts (a)-(c). f left parenthesis x right parenthesis equals StartFraction 1 Over x EndFraction (a) Use the formal definition to find the derivative of yequalsf(x) at xequals5. (b) Find f(5) and find the equation of the normal line at the point (5, f(5)). (c) Graph yequalsf(x) and the tangent line at the point (5, f(5)) in the same coordinate system. Question content area bottom Part 1 (a) The derivative of a function f at x, denoted by f prime left parenthesis x right parenthesis, is f prime left parenthesis x right parenthesis equals ModifyingBelow lim With h right arrow 0 StartFraction f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis Over h EndFraction provided that the limit exists. Use the definition of the derivative of f at x to find the derivative of the given function f(x) when xequals5. f prime left parenthesis 5 right parenthesisequalsModifyingBelow lim With h right arrow 0 StartStartFraction left bracket StartFraction 1 Over 5 plus h EndFraction right bracket minus left bracket StartFraction 1 Over x EndFraction right bracket OverOver h EndEndFraction Part 2 Evaluate the limit expression to find f prime left parenthesis 5 right parenthesis. f prime left parenthesis 5 right parenthesisequals negative StartFraction 1 Over 25 EndFraction (Type an integer or a fraction.) Part 3 (b) f left parenthesis 5 right parenthesisequals one fifth (Type an integer or a

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!