Question

find f(7) if f(x) = \frac{x^{3}}{21}-4x^{2}.
f(7) =
(simplify your answer.)

Explanation:

Step1: Find the derivative of \(f(x)\)

Use the power - rule \((x^n)^\prime=nx^{n - 1}\). For \(y=\frac{x^{3}}{21}-4x^{2}\), the derivative \(f^\prime(x)=\frac{3x^{2}}{21}-8x=\frac{x^{2}}{7}-8x\).

Step2: Substitute \(x = 7\) into \(f^\prime(x)\)

Substitute \(x = 7\) into \(f^\prime(x)\): \(f^\prime(7)=\frac{7^{2}}{7}-8\times7\).
First, calculate \(\frac{7^{2}}{7}=\frac{49}{7}=7\). Then, calculate \(8\times7 = 56\). So \(f^\prime(7)=7-56=-49\).

Answer:

\(-49\)