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How do you find the slope of the tangent line to the graph of the function #f(x)=3/2x+1# at (-2,-2)?

Answer 1

#m=3/2#

# f(x) = 3/2x + 1 # is a straight line, comparing with #y=mx+c# we see #m=3/2#, so the gradient of the tangent line is #3/2# everywhere.

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Answer 2

William Abdalla

To find the slope of the tangent line to the graph of the function f(x) = (3/2)x + 1 at the point (-2, -2):

Determine the derivative of the function f(x) with respect to x.
Evaluate the derivative at x = -2 to find the slope of the tangent line at that point.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.