2 years ago

Write a linear function f with the values f(0)=−3 and f(7)=11 A function is f(x)=

Mathematics

1 answer:

Rudik [331]2 years ago

4 0

Answer:

f(x) = 2x - 3

Step-by-step explanation:

x y

0 -3

7 11

when x = 0, y = -3. When x increases by 7, y increases by 14, or when x increases by 1, y increases by 2.

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shusha [124]

$\text{Hi there! :)}$

$\large\boxed{f'(2) = -\frac{16}{27} }$

$f'(x) = \frac{(5 + x^{2} )(-2x) - (7 - x^{2} )(2x)}{(5+x^{2})^{2} } \\\\f'(x) = \frac{-10x-2x^{3}- 14x + 2x^{3} }{(5+x^{2})^{2} } \\\\f'(x) = \frac{-24x}{(5+x^{2})^{2} }\\\\ \text{Solve for the derivative at f'(2) using substitution:}\\\\f'(2) = \frac{-24(2)}{(5+2^{2})^{2} } \\\\f'(2) = \frac{-48}{81} \\\\\text{Simplify:}\\\\f'(2) = -\frac{16}{27}$