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