Derivatives and Rates of Change

1. Find \(f'(a) \) where \(f(x) = 3x^2-5x+7 \).
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2. Find an equation of the tangent line to the curve \( y=\sqrt{x+3}\) at the point \((1, 2).\)
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3. Find an equation of the tangent line to the curve \( y=x^3-2x+3\) at the point \((1, 2).\)
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4. Find \(f'(a) \) where \(f(x) = \dfrac{1}{\sqrt{x+3}}\).
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5. Find \(f'(a) \) where \(f(t) = \dfrac{2t+1}{t+3}\).
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6. Find an equation of the tangent line to the graph of \( y=g(x)\) at \( x=4 \) if \( g(4)=-3\) and \( g'(4)=5 \).
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