I can't solve a question of a test of a pre-university mathematics course. I understand the rules of derivatives but I am blocked when trying to solve the following question below.
I tried to solve the question by making the derivative of the function and equaling that to the derivative in the question. So, I got that $a= \frac{21}{x^4}$ etc. But, I may not use those answers as solution for the question.
What am I seeing wrong or where am I blind? Could someone give me a start to solve this question?
This is the question:
If $$ f(x)=7x^3-2x^2+4x-11 $$ then de derivative $$ D(f(x))=ax^4+bx^3+cx^2+dx+e$$ What are the values for $a,b,c,d$ and $e$?
Thanks in advance.
The coefficients $a,b,c,d,e$ must be constants. They cannot be dependent on $x$. I think you've gotten hung up on the fact there seems to be a quartic term $(ax^4)$, which you feel shouldn't be there. You can make these terms disappear with zero-coefficients. By ordinary differentiation, you get that $$D(7x^3-2x^2+4x-11) = 21x^2-4x+4 = \underbrace{0}_{a}x^4 + \underbrace{0}_{b}x^3 + \underbrace{21}_{c}x^2 + \underbrace{(-4)}_{d}x + \underbrace{4}_{e} $$
Therefore, the values are $a = 0$, $b = 0$, $c = 21$, $d = -4$, and $e = 4$.