Question

Find f '(−3), if f(x) = (2x2 − 7x)(−x2 − 7). Round your answer to the nearest integer. Use the hyphen symbol, -, for negative values.

Answer 1

\(\large\color{black}{ \displaystyle f(x)=(2x^2-7x)(-x^2-7) }\)

Answer 2

\(\large\color{black}{ \displaystyle f'(x)=(2x^2-7x)'\times (-x^2-7)+(2x^2-7x)\times (-x^2-7)' }\)

Answer 3

\(\large\color{black}{ \displaystyle (2x^2-7x)' = \quad ?\\[0.7em] (-x^2-7)' = \quad ? }\)

Answer 4

By \('\) I am denoting [the first} derivative.

Answer 5

Then, when you find \(\large\color{black}{ \displaystyle f'(x) }\), plug in x=3.

Answer 6

You can find the f`(x) either using the product rule I proposed, or you can first expand and then differentiate. That doesn't matter.