The discussion revolves around the differentiation of the function f(x) = (x^2 + 5x + 2)^4 and the subsequent finding of the tangent line, specifically y = 160x + 16. Participants are examining the correctness of the derivative and the tangent line equation.
Some participants express uncertainty about their derivative results and whether they have made errors in their calculations. There is an ongoing exploration of the expressions involved in the differentiation process, with participants seeking clarification on specific steps and assumptions.
There appears to be confusion regarding the point at which the tangent line is evaluated, as well as the completeness of the derivative expression. Participants are encouraged to clarify these aspects to further the discussion.
madeeeeee said:f(x)=(x^(2)+5x+2)^(4)
f'(x)= 4(x^2 + 5x + 2)^3 (2x + 5)
Not okay.= 8x + 20(x^2 + 5x + 2)^3
Notice something missing in your expression? Do you really want to multiply only the 20 by (x2 + 5x + 2)3?madeeeeee said:f'(x)= 4(x^2 + 5x + 2)^3 (2x + 5)
= 8x + 20(x^2 + 5x + 2)^3
is this right
Where did you get this? Was there a point that was given?madeeeeee said:than my equation of the tangent turned out to be y=160x +16