Who is asking: Student
Level: Secondary
Question:
find the slope of the tangent to each curve at the given point
f(x)=square root 16-x, where y=5
Hi,
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}
Penny