Use the given definition to find (A): If F(x) = + ax + 2x2 + + anten is a polynomial function, then for a square matrix A, RA) = aol +374 +374? ++ Rx) = 4 - 9x + x? 1x) = 4 - ****, --17:) A) -16 0 It 14 4 1
Use the given definition to find f(A): If f(x) = a0 + 2 x + a2x2 + ... + ant is a polynomial function, then for a square matrix A, F(A) = aol + a1 A + a2A2 + ... + anA". 2o f(x) = 2 - 8x + x², A = 3 f(A) =
Let f(x) = 3x2 + 4 and g(x) = 2x − 4. Find the function. (g ∘ f)(x) =
[6 points] Suppose that f'(x) = 3x2 + 2x + 7 and f(1) = 11. Find the function f(x). Of(x) = x3 + x2 + 7x + 11 Of(x) = x3 + x2 + 7x + 2 Of(x) = 6x + 5 Of(x) = x3 + x2 + 9 10. V MY NOTES [6 points] Find the integral: 15x3/2 + 21n|x[ + c 10 x3/2 + 2\n\xl + C O 5x1/2 - + c şx-1/2 - + c
Problem 4.1 Dependent equations? Given: x +2x2 2x+3x, 5 2xx +3x-2x 18 -x, + 3x2 + x3-4x,--6 x 3x2+ 5x 5x, 13 If the set of 4 equations is dependent or independent Find:
(1 point) Given the function f(3) = 3x2 + 2x - 3 find the following (a) the average rate of change of fon (-4,1): -7 (b) the average rate of change of f on [1, 2+h]: 1
Find all rational zeros of the function f(x)=2x'-9x'-6x+5. Find all rational zeros of the function f(x)=2x'-9x'-6x+5.
5. Use the limit definition to find the derivative of f(x) = V3x + 2. (6 points) 6. Find the derivatives of the following functions. Do not simplify after taking the derivative. 5 points each a. f(x) = (4x2 +1) c. h(x) = arcsin(3x2+ 2x-1) b. h(x) = 3sec(x2)
2) Let f(x) = 3x2 - 2x +1. a. Find the average rate of change from x = 1 to x = 3 b. Find the equation of the secant line containing the points (1.f (1)) and (3,f(3)) c. Find the derivative of the function at the point x = 3 and determine the equation of the tangent line at that point.
9. Find the average value of f(x) = 3x2 - 2x on the interval [1,4]. (8 Points) Hint: Use the formula: favo = 6-a Srca) dx