f ( x ) is a linear function, f ( − 5 ) = − 2 , and f ( 5 ) = − 1 , find an equation for f ( x )
Find the linear approximation of given function at (0,0). 5.r + 2 f (x,y) 5y + 1 f(x, y)
(5 pts) 2. The linear function f(x) = mx + bis one to one for all slopes, except when = Then find /'(x). m70 **(x) = x m bom (5 pts) 3. The relative value of currencies fluctuates every day. On September 9, 2019, one Euro is worth 1.09 US dollars. €1 $1.09. Find a function, that gives the US dollar value f(x) of x Euros. (3 pts) for ay =1.09.8 . Find f(x). What does f'(x) represent? (3 pts)...
Consider the function f(x, y) = x^3 − 2xy + y^2 + 5. (a) Find the equation for the tangent plane to the graph of z = f(x, y) at the point (2, 3, f(2, 3)). (b) Calculate an estimate for the value f(2.1, 2.9) using the standard linear approximation of f at (2, 3). (c) Find the normal line to the zero level surface of F(x, y, z) = f(x, y) − z at the point (2, 3, f(2,...
6. The table shows some values of an exponential function, f. and a linear function, g. Find the equation for f(x) and g(x) and use the functions to complete the table. fx) g(x) 0 0.36 ? 2 0.216 8.2 3 ? ? 0.07776 5 13 8. Allowance Riddle Suppose a child is offered two choices to earn an increasing weekly allowance: the first option he can choose begins at 1 cent and doubles each week, while the second option begins...
1. Given the graph of the function f(x) below, find the following fi 6-5-421/4 2 345 6 -2 -6 The domain of f(x):The range of f(x): Interval(s) where f(x) is increasing: . The -intercept(s) of f() The value(s) of z for which f(x) 1 Interval(s) where f(x) is negative: . Is the function f(x) invertible? YES or NO (Circle one) Explain your reasoning: . The portion of the graph from z -1 to x-2 is linear. Find an equation for...
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.
Consider the function and the value of a. f(x) = -5 X - 1 a = 3 (a) Use mtan f(a+h) - f(a) = lim to find the slope of the tangent line mtan h0 h = f'(a). = mtan 5 4 (b) Find the equation of the tangent line to fat x = a. (Let x be the independent variable and y be the dependent variable.) »- 3 = (x – 3) x Consider the graph. у 5 x...
#3 Define a function f : [15] → [15] by f(1) = 3, f/2) = 5 f(3) = 4, f(4) = 2, +(5)=1, with f(x) L a linear between these points. Find a penod-2 point and the 2-cycle.
2. Suppose the linear approximation of a differentiable function f(x, y, z) at the point (1,2,3) is given by L(x, y, z) = 17+ 6(x – 1) – 4(y – 2) + 5(2 – 3). Suppose furthermore that x, y and z are functions of (s, t), with (x(0,0), y(0,0), z(0,0)) = (1, 2, 3), and the differentials computed at (s, t) = (0,0) are given by dx = 7ds + 10dt, dy = 4ds – 3dt, dz = 2ds...
For the piecewise linear function, find (a) f-3), (b) -2), (c) K0), (d) f(2), and (e) f(5) 2x ifxs-2 fix): x-2 ifx-2 (a) -3) (b) f-2)= (c) f(0)= (d) (2)= (e) 5)-