determine each of the following, where (f(x)=3.8x^{3}-4.9x - 4).\na. (f(8)=)\nb. (f(-5)=)

Explanation:

Step1: Find the derivative of f(x)

We use the power - rule $\frac{d}{dx}(x^n)=nx^{n - 1}$. For $f(x)=3.8x^{3}-4.9x - 4$, $f'(x)=3\times3.8x^{2}-4.9=11.4x^{2}-4.9$.

Step2: Calculate f'(8)

Substitute $x = 8$ into $f'(x)$. $f'(8)=11.4\times8^{2}-4.9=11.4\times64 - 4.9=729.6-4.9 = 724.7$.

Step3: Calculate f'(-5)

Substitute $x=-5$ into $f'(x)$. $f'(-5)=11.4\times(-5)^{2}-4.9=11.4\times25-4.9 = 285 - 4.9=280.1$.

Answer:

a. $724.7$ b. $280.1$