Question

If f(9) = 9 and f ´(9) = 1, then $( - \infty,0\rbrack$ is equal to –

• A. 0
• B. 1
• C. –1
• D. None of these

Answer 1

Answer: (B)

1

Answer 2

$\lim _ { x \rightarrow 9 } \frac { 3 - \sqrt { f ( x ) } } { 3 - \sqrt { x } }$ , $\frac { 0 } { 0 }$ ⇒ $\lim _ { x \rightarrow 9 } \frac { 0 - \frac { 1 f ^ { \prime } ( x ) } { 2 \sqrt { f ( x ) } } } { 0 - \frac { 1 } { 2 \sqrt { x } } }$

= + $\frac { f ^ { \prime } ( 9 ) } { 2 \sqrt { f ( 9 ) } }$ × $2 \sqrt { 9 }$ = $\frac { 1 \times 3 \times 2 } { 2 \times 3 }$ = 1