For the one-parameter family of functions defined for all real

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

For the one-parameter family of functions

g_t(x)=e^{t x}-t x

defined for all real

x

, explain whether there exists a non-zero real value of

t

for which

g_t

is concave down on the entire real line. State your conclusion.