Derivadas 8) Hallar, utilizando la definición, la pendiente de la recta tangente a la curva \( f(x)=x^{2}-2 \) en el punto \( P=(3 ; 7) \). Dar la ecuación de la recta y graficar la curva y la recta.

Hallar \( y_{1} \) \( y=\frac{x^{2}}{\sqrt[3]{x^{2}+4}} \)

\( f(x)=3 x^{2}+6 x-45 \) A. The parabola opens downward and has a maximum value of -48 . B. The parabola opens upward and has a minimum value of (c) What is the range of \( f(x) \) ? The range of \( f(x) \) is \( [-48, \infty) \). (Type your answer in interval notation. Use integers or fractions for any nungibers in the expression.) (d) On what interval is the function increasing? The function is increasing on \( (-1, \infty) \). (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) On what interval is the function decreasing? The function is decreasing on \( \square \). (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

\( \left. \begin{array} { l } { \lim _ { h \rightarrow 0 } \frac { f ( a + h ) - f ( a ) } { h } } \\ { f ( x ) = x ^ { 2 } - 1 , \quad a = 0 } \end{array} \right. \)

If \( g(x) = e^{2x} \), find \( g(3) \).

یک تابع زیر را با استفاده از تقسیم طویل انتگرال بگیرید: \( \frac{x^{3} + 2x^{2} + 1}{x + 1} \)