Question

Suppose that f(x)=9x4/5−2x5/7. Evaluate each of the following:

f′(3) =

f′(6) =

Answer 1

Given $f(x)=9x^{\frac{4}{5}}-2x^{\frac{5}{7}}$ then;

$f'(x)=\frac{36}{5}x^{-\frac{1}{5}}-\frac{10}{7}x^{-\frac{2}{7}}=\frac{36}{5x^{\frac{1}{5}}}-\frac{10}{7x^{\frac{2}{7}}}$

$f'(x)=\frac{36}{5x^{\frac{1}{5}}}-\frac{10}{7x^{\frac{2}{7}}}$ .

Then

$f'(3)=\frac{36}{5(3)^{\frac{1}{5}}}-\frac{10}{7(3)^{\frac{2}{7}}} \approx4.736025022$

$f'(6)=\frac{36}{5(6)^{\frac{1}{5}}}-\frac{10}{7(6)^{\frac{2}{7}}} \approx 4.175359577$