Let $f ( x ) = 3 x ^ { 2 } - 5$ Which of the following is equal to $\lim _ { h \rightarrow 0 } \frac { f ( 1 + h ) - f ( 1 ) } { h }$ ?

A)-6
B)-1
C)1
D)6
E)Does not exist

Question

Let $f ( x ) = 3 x ^ { 2 } - 5$ Which of the following is equal to $\lim _ { h \rightarrow 0 } \frac { f ( 1 + h ) - f ( 1 ) } { h }$ ?

A)-6
B)-1
C)1
D)6
E)Does not exist

Quizplus · Accepted Answer

The expression $\lim _ { h \rightarrow 0 } \frac { f ( 1 + h ) - f ( 1 ) } { h }$ is the definition of the derivative of $f(x)$ at $x = 1$. Calculating $f(1+h) = 3(1+h)^2 - 5$ and $f(1) = 3(1)^2 - 5$, then substituting these into the limit and simplifying will give the derivative of $f(x)$ at $x = 1$, which is $6$.

Let f(x)=3x2−5f ( x ) = 3 x ^ { 2 } - 5f(x)=3x2−5

Let $f ( x ) = 3 x ^ { 2 } - 5$