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babymother [125]
3 years ago
13

At what point of the curve y = cosh(x does the tangent have slope 2?

Mathematics
1 answer:
Dahasolnce [82]3 years ago
5 0
The hyperbolic cos (cosh) is given by
cosh (x) = (e^x + e^-x) / 2
The slope of a tangent line to a function at a point is given by the derivative of that function at that point.
d/dx [cosh(x)] = d/dx[(e^x + e^-x) / 2] = (e^x - e^-x) / 2 = sinh(x)
Given that the slope is 2, thus
sinh(x) = 2
x = sinh^-1 (2) = 1.444

Therefore, the curve of y = cosh(x) has a slope of 2 at point x = 1.44
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The given line passes through the points and (4,1).
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Hey there! :)

Answer:

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Step-by-step explanation:

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Plug in two coordinates:

m = \frac{1-(-3)}{4-(-4)}

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Therefore, the slope of the line is 1/2.

A line that is perpendicular contains a slope that is the negative reciprocal. Therefore:

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Plug the slope into the point-slope formula:

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