Let and for all real .

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let

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

and

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

for all real

t

. (i) Obtain an expression for

\dfrac{dy}{dx}

in terms of

t

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

t

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

Related theory

Advanced Differentiation
Implicit and Parametric Differentiation
Derivatives of parametric functions
Continuity and Differentiability

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