Consider the functions and

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Consider the functions

f(x)=x^{4}

and

g(x)=e^{2x}

. At

x=0

, which function is more concave up? (a)

f

, because

f''(0)=12

while

g''(0)=4

. (b)

g

, because

g''(0)

is greater than

f''(0)

. (c)

g

, because

g''(0)=2

is greater than

f''(0)=0

. (d)

f

, because the graph of

x^{4}

opens upward, so it must be more concave up at

x=0

than

e^{2x}