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Sladkaya [172]
2 years ago
13

If a gradient of line a is 4 what is the gradient of the line perpendicular to a

Mathematics
1 answer:
katovenus [111]2 years ago
5 0
\bf \textit{perpendicular, negative-reciprocal slope for}\quad 4\implies \cfrac{4}{1}\\\\
negative\implies  -\cfrac{4}{ 1}\qquad reciprocal\implies - \cfrac{ 1}{4}
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================================================

Work Shown:

Compute the function value at the endpoints

f(x) = \sqrt{4-x}\\\\f(-5) = \sqrt{4-(-5)} = 3\\\\f(4) = \sqrt{4-4} = 0\\\\

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f'(c) = \frac{f(b)-f(a)}{b-a}\\\\f'(c) = \frac{f(4)-f(-5)}{4-(-5)}\\\\f'(c) = \frac{0-3}{9}\\\\f'(c) = -\frac{1}{3}\\\\

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Use algebra to solve for c

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