Quandaries and Queries

Who is asking: Student
Level: Secondary

find the slope of the tangent to each curve at the given point

f(x)=square root 16-x, where y=5


The slope of the tangent line at a point x=a on the curve y = f(x) is the value of the derivative of f at a, that is f'(a). Thus you need to find the derivative of f(x) and evaluate it at x=a.

f(x) = (16 - x) 1/2 and hence the derivative is f'(x) = 1/2 (16 - x) -1/2 (-1) (The -1 come from using the chain rule and differentiating 16 - x.) You have a = 5 and hence the slope of the tangent is f'(5) = -1/2 (11) -1/2


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