Section 2.7: Derivatives and Rates of Change

Find \(f'(a) \) where \(f(x) = 3x^2-5x+7 \).

Find an equation of the tangent line to the curve \( y=\sqrt{x+3}\) at the point \((1, 2).\)

Find an equation of the tangent line to the curve \( y=x^3-2x+3\) at the point \((1, 2).\)

Find \(f'(a) \) where \(f(x) = \dfrac{1}{\sqrt{x+3}}\).

Find \(f'(a) \) where \(f(t) = \dfrac{2t+1}{t+3}\).

Find an equation of the tangent line to the graph of \( y=g(x)\) at \( x=4 \) if \( g(4)=-3\) and \( g'(4)=5 \).