Provide an appropriate response.
-Find all points $( x , y )$ on the graph of $f ( x ) = 2 x ^ { 2 } - 3 x$ with tangent lines parallel to the line $y = 13 x + 5$.
A) $( 4,32 )$
B) $( 0,0 ) , ( 4,20 )$
C) $( 8,20 )$
D) $( 4,20 )$

Question

Quizplus · Accepted Answer

The line $y=13x+5$ has a slope of 13. For a tangent line to be parallel to this line, it must also have a slope of 13. The derivative of $f(x)$ is $f'(x)=4x-3$. Setting this equal to 13 and solving for x, we get $x=4$. Plugging this into the original function, we get $f(4)=32$. Therefore, the only point on the graph that satisfies the given conditions is $(4,20)$, and the answer is D.

Provide an Appropriate Response (x,y)( x , y )(x,y) On the Graph Of

Provide an Appropriate Response $( x , y )$ On the Graph Of