+73 Consider the function \(y=g(x) = -x^{2}+7x+6\).
(a) Use the limit definition to compute a formula for \(y=g'(x)\).
y = ?
+129899 g ( x + h) - g (x)
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h
- ( x + h)^2 + 7 (x + h) + 6 - [ -x^2 + 7x + 6 ]
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h
- [ x^2 + 2xh + h^2] + 7x + 7h + 6 + x^2 - 7x - 6
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h
-x^2 - 2xh - h^2 + 7x + 7h + 6 + x^2 - 7x - 6
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h
-2xh + 7h - h^2
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h
h ( -2x + 7 - h)
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h
-2x + 7 - h let h → 0
-2x + 7
