5x² + x 7) (15 pts) Given f(x) = calculate f'(x). 5-435
4) (15 pts) Given f(x) = -3xº + 5x3 + 3x + V5, calculate f'(x). 5) (15 pts) Given g(x) = 5x3 +67x + m - 2e*, calculate g'(x). 6) (15 pts) Given h(x) = (3x2 + 5e*)(6x4 + 3Vx), calculate h'(x).
Find the derivative of the following function. f(x) = (2x - 3)(3x4 +7x) f'(x) = 2(3x4 + 7x)+(2x - 3)(12x3 +7) f'(x) = 2 + (12x3 + 7) f'(x) = 2(12x3 + 7) f'(x) = 2(3x4 +7x) – (2x - 3)(12x3 + 7)
Find the requested composition of functions. Given f(x) = 4x2 + 3x + 6 and g(x) = 3x - 8, find (g ∘ f)(x).
Find the derivative of f(x) = 3x4 - 8x2+2x–7.
7. (15 pts) Numerical Integration. Given a continuous function f (x) on the interval [a, b], write the Lagrange form of the quadratic polynomial interpolating f(a), (a b)), f(b). Instead of calculating the integral I(f) Jaf(x)dx we could approximate it via Q(f) = | q(x)dx. Find an expression for this quadrature rule, the so-called Simpson's rule.
(15 pts) 7) Using the Divergence Theorem, calculate the flux integral JSF dĀ where F(x, y, z) =< 2 + x2,r2 + y2y +> and S is the closed cylinder 22 + y2 = 1 with 03:31.
Given f(x)=2x1/4x2/4, calculate the revenue function, the profit function, (WyWyp) (2,18,20), (wi W2.p) (4,18,20), and plot the lsoprofit lines with the given data and production function 1.
Question 15 (5 points) Determine the domain and the range of the function. f(x) = 4x2 - X-3 A
Given f(x) = 3x3 + 4x2 + 4x + 3. Find (-1)'0).