Find a function f that has derivative $f ^ {t } ( x ) = 12 x - 6 \text { and with graph passing through }$ the point (5,6).
A) $f ( x ) = \frac { 6 } { 25 } x ^ { 2 }$
B) $f ( x ) = 12 x ^ { 2 } - 6 x - 112$
C) $f ( x ) = 6 x ^ { 2 } - 6 x - 111$
D) $f ( x ) = 6 x ^ { 2 } - 6 x - 114$
E) $f ( x ) = \frac { 6 } { 5 } x$

Question

Find a  function f that has derivative $f ^ {t } ( x ) = 12 x - 6 \text { and with graph passing through }$ the point (5,6). 
A) $f ( x ) = \frac { 6 } { 25 } x ^ { 2 }$
B) $f ( x ) = 12 x ^ { 2 } - 6 x - 112$
C) $f ( x ) = 6 x ^ { 2 } - 6 x - 111$
D) $f ( x ) = 6 x ^ { 2 } - 6 x - 114$
E) $f ( x ) = \frac { 6 } { 5 } x$

Quizplus · Accepted Answer

Since the derivative of f is 12x - 6, we know that f is some polynomial of degree 2 since the degree of the derivative is 1 less than the degree of the original function. We can also determine the constant of integration by plugging in the given point (5,6). Using the power rule in reverse, we can say that f(x) = 2x^2 - 6x + C, where C is our constant of integration. Plugging in the point (5,6), we get 6 = 2(5^2) - 6(5) + C, which simplifies to C = -114. Thus, the final answer is f(x) = 2x^2 - 6x - 114, which corresponds to choice D.

Find a Function F That Has Derivative ft(x)=12x−6 and with graph passing through f ^ {t } ( x ) = 12 x - 6 \text { and with graph passing through }ft(x)=12x−6 and with graph passing through

Find a Function F That Has Derivative $f ^ {t } ( x ) = 12 x - 6 \text { and with graph passing through }$