Math CentralQuandaries & Queries


Question from Amanda, a student:

If f(x)=square root of (x+4), and the slope of the tangent line at x=21 was 1/n for some integer n, then what would you expect n to be?

Hi Amanda.

The derivative of f evaluated at x=21 will tell you the slope at that point.

if f(x) = sqrt(x+4), then f'(x) = 1 / [ 2 (sqrt(x+4) ].

Thus f'(21) = 1 / [ 2 (sqrt(21+4) ] = 1 / 10.

If 1 / 10 = 1 / n , then n is 10, and that is indeed an integer.

Stephen La Rocque

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