
7) (15 pts) Given f(x) 4x2+x 6-3x4 calculate f'(x).
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).
Define the
function f : Rf3 ! Rf5 by
f(x)= 5x/x-3Prove: f is surjective ("onto"
R\5).
R {5} by 7. (15 pts) Define the function f : R\{3} f(x) = 0 Prove: f is surjective ("onto" R\{5}). I
a force is experimentally shown to be given F(x)=5x^2-6x^7 [N]. Calculate the work done by the force over a distance 0.5m
Question 6 5 pts Let f(x) = x + 5x Find a value с between x = 0 and X= 7 so that the average rate of change of f(x) from x = 0 to X = 7 is equal to the instantaneous rate of change of f(x) at X=C . You may use the fact that f'(x) = 3x2 + 5.
Question 32 Find (fg)(x). f(x)= 3x g(x)= 5x+ 7 O None of these og)(x)= x/15+21x O [g)(x)= 15x2 + 7 o Vg)(x)= V8x+ 7 O V&)x)15x2+ 21x og)(x)=xV15+/21x Question 41 1 pts List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which actually are zeros). Q(x)=x*- 4x- 5x+8 O 1.8 - 1. - 2. - 4.-8 Ot1.18 None of the above O 1.2.4,8 O +1.2+4,18
Question 15 1 pt 1 Details -3.2 - 7 Given the function f(x) = - 2x2 + 2x + 11 32 +4 Calculate the following values: <-3 -3<<4 f(4) = f(10) = f(-3) = fl - 9) = f(1) = f(2) = Question 16 1 pt 1 Details Find the average rate of change for the given function over the indicated values of x. If necessary, round your final answer to two decimal places. y = 5x + 7, where...
9. The linear function f is defined by f(x,y) = (x + 2y, 5x - y). (a) (5 pts) If ū=(-1,2) and 7 =(3, 1), check that fü+v) = f(ū) + f(ū). (b) (10 pts) Find the standard matrix for f.
(5 pts) Let f(x)=-3x? +5x+2. Evaluate and fully simplify the difference quotient f(x+h)-f(x) h You must show all work to receive credit.
Given that f(x) = 3x + 1 g(x) = 5x - 8 and h(x) = 2x – 1 3 Find:- i) f(-4) = ii) g[h(5)] = iii) f[g(3)] = iv) g[h(x)] = vi) h-1(7) =