The point at which the slope of the tangent line is -3

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12-01-2018
Mathematics

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The point at which the slope of the tangent line is -3

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altavistard altavistard · Answer 1 · 2018-01-12T04:33:13+01:00

f(x) = 6x^2 + 3x - 6

The derivative, and thus the slope of the T. L. to the graph, is f '(x) = 12x + 3. Set this result = to -3 and solve for x:

12x + 3 = -3 => 12x = - 6 and x = -1/2
6 + 6 - 24
If x = -1/2, y = f(-1/2) = 6(1/4) - 3(-1/2) - 6 = ----------------- = -6
4

The slope of the T. L. to the graph will be -3 at the point (-1/2, -6).