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Derivatives, Difference Quotient and Equation of a Tangent Line

Compute the derivative of the function using the difference quotient and find the equation of the line that is tangent to its curve for x=c

1. f(x) = x^2-3x+2; c=1

2. y = (x+7)/(5-2x); c=1

Find the first and second derivative for for the next 3 problems

1. y=6x^5-4x^3-5x^2-1

Solution Preview

1. f(x) = x^2-3x+2; c=1
(f(x)-f(y))/(x-y) = ((x^2-3x+2)-(y^2-3y+2))/(x-y)
=((x^2-y^2)-3(x-y))/(x-y)=x+y-3 = 2x-3 as y->x
So f'(x)=2x-3
When x=c=1, ...

Solution Summary

Derivatives of functions are found using the difference quotient and the equation of the line that is tangent to its curve for x=c s found. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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