For , determine the concavity of the graph at…

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

Problem

For

f(x)=x^{3}-3x^{2}+2

, determine the concavity of the graph at

x=1

. (a) Concave up at

x=1

because

f''(1)>0

. (b) Neither concave up nor concave down at

x=1;\;f''(1)=0

and

f''

changes sign. (c) Concave down at

x=1

because

f'(1)<0

. (d) Cannot be determined because

f''(1)=0

but

f''

does not change sign.