SOLUTION: The equation of the tangent line to the graph of f(x) at x=2 is y=(-1/4)x+5. Find f'(2).

Question 789297: The equation of the tangent line to the graph of f(x) at x=2 is y=(-1/4)x+5.
Find f'(2).
Answer by fcabanski(1391) (Show Source): You can put this solution on YOUR website!
y=mx+b is the slope intercept form of a line equation. m is the slope. The derivative of a function at a point is the slope of the tangent line to the function at that point.

In other words, if you know the equation of the tangent line to a function is y=mx+b, then the value of the derivative of the function at that point x is f'(x) = m, the slope of the tangent line to the function at that point.

In this case the slope of the tangent line to the function at x=2 is -1/4. That means the value of the derivative of the function at x=2 is -1/4. f'(2) = -1/4.

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