Consider the curve where is a real constant

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Consider the curve

x=t^{2},\;y=t^{4}+kt

where

k

is a real constant. (i) Find the value of

t

(in terms of

k

) at which the curve can have an inflection point. (ii) Determine all real values of

k

for which such an inflection point actually exists.

Related theory

Higher-Order Derivatives
Advanced Differentiation
Implicit and Parametric Differentiation
Derivatives of parametric functions
Continuity and Differentiability

Browse the problem library