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1 month ago

At what point of the curve y = cosh(x) does the tangent have slope 3?

Mathematics

1 answer:

PIT_PIT [12.4K]1 month ago

3 0

Answer:

(1.82, 3.17)

Step-by-step explanation:

Starting with the equation of the curve:

y = cosh(x)

We must find the point where the tangent line has a slope of 3. The slope of the tangent at any given point on a curve can be derived from its derivative.

dy/dx = sinh(x) = 3

Based on the graph of sinh(x), we find:

x ≈ 1.82

Substituting this value into cosh(x) gives:

y = cosh(1.82) ≈ 3.17

Thus, at the coordinates (1.82, 3.17), the tangent exhibits a slope of 3.

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