find f(-4) if f(x) = \\frac{x^{3}}{7}-5x.\nf(-4)= (simplify your answer. type an integer or a fraction.)

Explanation:

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

Use the power - rule ((x^n)^\prime=nx^{n - 1}). For (y=\frac{x^{3}}{7}-5x), the derivative (f^\prime(x)=\frac{3x^{2}}{7}-5).

Step2: Substitute (x = - 4) into (f^\prime(x))

(f^\prime(-4)=\frac{3\times(-4)^{2}}{7}-5). First, calculate ((-4)^{2}=16). Then (3\times(-4)^{2}=3\times16 = 48). So (f^\prime(-4)=\frac{48}{7}-5).

Step3: Rewrite 5 with a denominator of 7

(5=\frac{35}{7}), then (f^\prime(-4)=\frac{48}{7}-\frac{35}{7}=\frac{48 - 35}{7}=\frac{13}{7}).

Answer:

(\frac{13}{7})