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Katie's question at Yahoo! Answers regarding a function and its given tangent line

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MarkFL

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Feb 24, 2012
13,775
Here is the question:

If an equation of the tangent line to the curve y=f(x) at the point where a=2 is....?


y=4x-5, find f(2) and f'(2)

Please walk me through this question step by step.
I have posted a link there to this topic so the OP can see my work.
 
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MarkFL

Administrator
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Feb 24, 2012
13,775
Hello Katie,

Consider the following diagram, showing the function $f(x)=x^2-1$ and its tangent line $y=4x-5$:

katie.jpg

As you can see, the instantaneous slope of the function must match the slope of the tangent line at the point of tangency, and the value of the function at that point must be equal to the value of the tangent line at that point since they touch there. Hence, we must have:

\(\displaystyle f'(2)=\frac{d}{dx}(4x-5)=4\)

\(\displaystyle f(2)=y(2)=4(2)-5=3\)