For a differentiable function

MATHEMATICS · Single correct · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

Problem

p

, the average rate of change over

[1,1+h]

\dfrac{p(1+h)-p(1)}{h}=7+0.5h

for all sufficiently small non-zero

h

. Which statement is most strongly supported by this information? (a)

p'(1)=0

because the expression depends on

h

. (b)

p'(1)=0.5

because the coefficient of

h

0.5

. (c)

p'(1)=7

because the average rates approach

7

h \to 0

. (d)

p'(1)

is undefined because

\dfrac{p(1+h)-p(1)}{h}

changes with

h