Consider the function \( f(x)=\frac{2}{x^{2}}-\frac{7}{x^{7}} \). Let \( F(x) \) be the antiderivative of \( f(x) \) with \( F(1)=0 \). Then \( F(x)= \)

Graph the polynomial function \( f(x)=2 x^{4}+12 x^{3}-18 x^{2}-108 x \). Answer parts (a) through (e). (d) Determine the maximum number of turning points on the graph of the function. The graph of the function will have at most (e) Use the information in parts (a) through (d) to draw a complete graph of the function by hand. Choose the

Graph the polynomial function \( f(x)=2 x^{4}+12 x^{3}-18 x^{2}-108 x \). Answer 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. The \( x \)-intercept(s) is/are \( \square \). (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each answer only once.) The \( y \)-intercept is \( \square \). (Type an integer or a simplified fraction.) (c) Determine the 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 zero(s) of \( ~ \) is/are (Tvne an intener \( n \).

Find the integral. \( \int x^{6} d x \)

Approximate the area under the graph of \( f(x) \) and above the \( x \)-axis using \( n \) rectangles. \( f(x)=x^{2}+2 \); interval \( [0,5] ; n=5 \); use left endpoints A. 40 B. 32 C. 65 D. 66

Find the integral. \( \int\left(x^{4}-2 x^{3}\right)^{4}\left(4 x^{3}-6 x^{2}\right) d x \)