So I'm having trouble trying to solve this. I have been puzzling over it. I know I need to use the slope of the parallel line to find the derivative but I just can't seem to work it out in my head. I need to find the equation of the tangent line of: $$f(x)=−4x^2+11x−2 $$ at $$x=2$$ that is parallel to $$ y=-5x-1$$
2026-03-30 04:00:16.1774843216
Finding equation of tangent line at a point parallel to another function
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Firstly, we find the derivative to be $f'(x)=-8x+11$. At the point $x=2$, the derivative is equal to $-5$ (found by evaluating the derivative at this point), which tells us the slope of the tangent line. Since this and the slope of the given line are the same, then we just have to find an equation for this line. At $x=2$, the y-value of the function is $4$. Since we know the slope and a point, we can find the equation of the line to be $(y-4)=-5(x-2)$.