14 years ago
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Derivative problem (restated upon request)?

let me put the question in its original form so you can see what I mean. For this problem use the definition of the derivative to compute the derivative of the given function. g(x)=3x-7 then use the derivative found in the previous part to answer this question. Find the equation of the tangent line to h(x)=3x-7 at x=-13 PLEASE HELP
Top 3 Answers
14 years ago
Bob G
Favorite Answer
The slope of the tangent line is equal to the derivative, which is 3 (found via the power law). You also need to figure out either y intercept or the x intercept. Seeing as how this is a straight line, the easy thing to do is to find the y intercept. Substitute a 0 for the x and solve. In this case, the y intercept is -7. That makes the equation of the tangent line: y = 3x - 7. Since the function is a straight line, the equation of the tangent line is the same everywhere, including when x = -13. Finding the tangent line for a straight line is kind of lame, which is probably why someone wanted the question restated. It doesn't make sense. Normally, the equation of the tangent line is found for a curve. For the record, the x intercept is found by solving for 0 = 3x - 7.
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14 years ago
gitter1226
The definition of a derivative is this: f'(a) = limit (as h approaches 0) of ( [f(h + a) - f(a)] / h ) g(x) = 3x - 7 g'(x) = limit (h -> 0) ( [g(h + x) - g(x)] / 0 ) g'(x) = limit (h -> 0) ((3x + 3h - 7 - (3x + 7)) / h) g'(x) = limit (h -> 0) (3h / h) g'(x) = limit (h -> 0) (3) g'(x) = 3 I'll leave the rest to you.
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14 years ago
Anonymous
so use the limits definition...okay read your book then upon finding the limit subsitute the limit into y=mx+b where the limit equals m, subtitute g(x) when x = the limit.. and that's about it
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