Please help:))
Determine the slope of the tangent line of the function f(x)= x+3/x+2 at the point
(-1, 2).
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Please help:))
Determine the slope of the tangent line of the function f(x)= x+3/x+2 at the point
(-1, 2).
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Answer:
To find the slope of the tangent line to the function f(x) at the point (-1, 2), we need to take the derivative of f(x) and evaluate it at x = -1.
We start by using the quotient rule to find the derivative of f(x):
f'(x) = [(x+2)(1) - (x+3)(1)]/(x+2)^2
= -1/(x+2)^2
Now we substitute x = -1 into the expression for f'(x) to get the slope of the tangent line at the point (-1, 2):
f'(-1) = -1/1^2 = -1
Therefore, the slope of the tangent line to f(x) at the point (-1, 2) is -1.
Step-by-step explanation: