Mathematics

Problem

Let

x=e^{t}+e^{-t}

and

y=e^{t}-e^{-t}

for all real

t

. a. (i) Obtain an expression for

\dfrac{dy}{dx}

in terms of

t

. b. (ii) Show that the curve has no horizontal tangents. c. (iii) Determine all real values of

t

at which the curve has a vertical tangent, and find the corresponding point(s). d. (iv) Write the equation(s) of the vertical tangent line(s) found in part (iii).

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