Calculate the derivative of the function. Then find the value of the derivative as specified.
-$$f ( x ) = x ^ { 2 } + 7 x - 2 ; f ^ { \prime } ( 0 )$$
A) $f ^ { \prime } ( x ) = 2 x + 7 ; f ^ { \prime } ( 0 ) = 7$
B) $f ^ { \prime } ( x ) = x + 7 ; f ^ { \prime } ( 0 ) = 7$
C) $f ^ { \prime } ( x ) = 2 x ; f ^ { \prime } ( 0 ) = 0$
D) $f ^ { \prime } ( x ) = 2 x - 2 ; f ^ { \prime } ( 0 ) = - 2$

Question

Quizplus · Accepted Answer

To find the derivative of the function, we need to use the power rule and the constant multiple rule of differentiation.

Power rule: if f(x) = x^n, then f'(x) = nx^(n-1)
Constant multiple rule: if f(x) = cx, then f'(x) = c

Using the above rules, we get:

f(x) = x^2 + 7x - 2
f'(x) = 2x + 7

To find f'(0), we just substitute x=0 in the above equation:

f'(0) = 2(0) + 7 = 7

Therefore, the best choice is A.

Calculate the Derivative of the Function f(x)=x2+7x−2;f′(0)f ( x ) = x ^ { 2 } + 7 x - 2 ; f ^ { \prime } ( 0 )f(x)=x2+7x−2;f′(0)

Calculate the Derivative of the Function $f ( x ) = x ^ { 2 } + 7 x - 2 ; f ^ { \prime } ( 0 )$