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Lebl-Basic-Analysis-I
· Problem 5.4.8
The Riemann Integral
Mathematics · logarithm-exponential
Problem
Show that
e
x
e^x
e
x
is convex, in other words, show that if
a
≤
x
≤
b
a \leq x \leq b
a
≤
x
≤
b
, then
e
x
≤
e
a
b
−
x
b
−
a
+
e
b
x
−
a
b
−
a
.
e^x \leq e^a \frac{b-x}{b-a} + e^b \frac{x-a}{b-a}.
e
x
≤
e
a
b
−
a
b
−
x
+
e
b
b
−
a
x
−
a
.
Related theory
The Complex Exponential And Logarithm
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