If the point \( (1,2) \) is an inflection point of the curve of the function \( f \) where \( f^{\prime}(x)=4 x^{3}-\mathrm{k} x^{2} \), then \( \mathrm{k}=\ldots \ldots \) (a) 24 (b) 6 (c) 4 (d) 12

\( \int _{}^{}\frac{x^{2}}{\sqrt [4]{x^{3}}+2} d x \)

El área encerrada por las curvas \( y=x, y=a, y=-x \) es?

Find the general indefinite integral. (Use \( C \) for the constant of integration. \[ \int 5 v\left(v^{2}+2\right)^{2} d v \]

Graph the polynomial function \( f(x)=-2(x-2)^{2}\left(x^{2}-9\right) \) using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph of f behaves like \( y=\square \) for large values of \( |x| \). (b) Find the \( x \) - and \( y \)-intercepts of the graph of the function. (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) The \( y \)-intercept is \( \square \). (Simplify your answer. Type an integer or a fraction.) (c) Determine the real zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the \( x \)-axis at each \( x \)-intercept. The real zero(s) of \( f \) is/are \( \square \).

\( \int \frac { d x } { 4 x ^ { 2 } + 25 } \)