Mostrar que toda función definida en el intervalo \( f:[0,1] \rightarrow[0,1] \) tiene un punto fijo

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

Explique o Teorema Fundamental do Cálculo e como ele relaciona a diferenciação e a integração.

91. \( f(\theta)=\frac{6\left(2-\theta^{3}\right)}{3-2 \theta} \)

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

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