To solve the provided problems, we need to approach them one by one, using differentiation and the concepts of calculus. 1. First Derivative of ( h(x) ) Given: ( g(x) = 3 - x ) ( f(x) = \frac{6x^2}{3x - 9} ) ( h(x) = f(x) \cdot g(x) ) Finding ( h'(x) ): Calculate ( f(x) ): Simplify ( f(x) ). [ f(x) = \frac{6x^2}{3x - 9} = \frac{6x^2}{3(x - 3)} = 2x^2/(x-3) ] Product Rule for ( h(x) ): ( h(x) = f(x) \cdot g(x) ) [ h'(x) = f'(x) \cdot g(x) + f(x) \cdot g'(x) ] Find ( f'(x) ): Use the quotient rule. [ f'(x) = \left( \frac{d}{dx} 2x^2 ight) \frac{1}{x-3} + 2x^2 \cdot \frac{d}{dx} \left( \frac{1}{x-3} ight) ] Find ( g'(x) ): [ g(x) = 3 - x \implies g'(x) = -1 ] Substitute and Simplify: [ h'(x) = f'(x) \cdot (3 - x) + \frac{2x^2}{x-3} \cdot (-1) ] After substituting the derivatives, simplify this expression. 2. Equation of the Tangent Line at A(4, -2) Given: Curve: ( y = 2x^2 - 4x - 6 ) Find the derivative to get the slope at point ( A(4, -2) ): Find ( y'(x) ): [ y'(x) =