(CPMK1,2/C2,3,4/30). Seorang pengusaha ingin memaksimumkan fungsional keuntungan \( \quad \int_{0}^{T} \pi(x) d t \), dengan \( \pi(x)=x p(x)-\left(a x^{2}+b x+c\right) \). Dengan menggunakan konsep persamaan Euler, maka tentukanlah tingkat produksi optimal \( x^{*}(t) \)

Find relative Extreme values of \( F(x)=\frac{1}{4}-x^{3}-3 x \)

Calculate the area under the curve defined by the function \( f(x) = x^3 + 2x - 1 \) from \( x = 1 \) to \( x = 3 \).

Solve the equation: \( e^{2x} = 7 \)

Consider the function \( f(x) = x^2 \). Use the Fundamental Theorem of Calculus to compute the definite integral from 1 to 3.

Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then, use a calculator to obtain a decimal approximation for the solution. \( e^{1-5 x}=851 \) The solution set expressed in terms of logarithms is (Use a comma to separate answers as needed. Simplify your answer. Use integers or fractions for any numbers in the expression. Use In for natural logarithm and log for common logarithm.) Now use a calculator to obtain a decimal approximation for the solution. The solution set is \{ (Use a comma to separate answers as needed. Round to two decimal places as needed.)