If fis differentiable on(a,b) then it is also continuous on (a,b) and the absolute maximum and...
The graph of the function fis shown in the accompanying figure. (a) is f continuous at x = O No Why or why not? (Select all that apply.) Fa) is not defined lim Fx) - Fla) Olim Rx) does not exist limFX) exists There is a corner at x = pa) is defined Fx) exists F"(x) does not exist (b) is f differentiable at x = a? Justify your answer. (Select all that apply.) lim, Fx) exists lim FX) does...
Problem 2. (12 pts) The graph of a function fis given below. Answer the questions that follow. 110 6 2- 5 -6- - X-2 (i) (6 pts) Find the following limits. If a limit is infinite or does not exist, specify so. (Ipt each) a) lim f(x) = b) lim f(x)= c) limf(x) = d) lim f(x) = e) lim f(x) = g) limf(x) = (2 pts) Does f have any asymptote(s)? If yes, what kind? Write their equations. (iii)...
Find the results of next functions 2.-Find the values of a and b such that fis differentiable at x 1 ax+b si 1s. Sol, a- 2, b-1. f(x)=1si x<1 x-7 si 0<x Sb| f(x) =16/x si x< 3 If ... a) decide a value of b far which f is continuous b)fis differentiable in the value of b that ycu find in part a)? 4.- In the following functions determine what is requested sen(x) si x < mx+b si x...
1. Determine whether the statement is true or false. If false, explain why and correct the statement (T/FIf)exists, then lim ()f) o( T / F ) If f is continuous, then lim f(x) = f(r) (TFo)-L, then lim f(x)- lim F(x) "( T / F ) If lim -f(x)s lim. f(x) L, then lim f(x)s 1. "(T/F) lim. In x -oo . (T/F) lim0 ·(T / F ) The derivative f' (a) is the instantaneous rate of change of y...
For the graph of a function y = f(x) shown to the right, find the absolute maximum and the absolute minimum, if they exist. Identify any local maxima or local minima. Select the correct answer below and, if necessary, fill in the answer boxes to complete your choice. A. The absolute maximum of y= f(x) is f(_______ ) = _______ (Type integers or simplified fractions.) B. There is no absolute maximum for y = f(x). For the graph of a function y = f(x) shown...
Find the absolute extrema of the function, if they exist, over the indicated interval. Also indicate the x-value at which each extremum occurs. If no interval is specified, use the real numbers, (-00,00) f(x) = 0.001x2 + 4.2x-10 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The absolute maximum is at x = and the absolute minimum is at x = (Use a comma to separate answers as needed.)...
Find the absolute maximum and absolute minimum values of the function, if they exist, on the indicated interval. f(x) = x2 - 4x + 10; [-2,4] O A. Absolute maximum is 22; absolute minimum is 10 OB. Absolute maximum is 10; absolute minimum is 6 OC. Absolute maximum is 22; absolute minimum is 6 OD. There are no absolute extrema.
Question 1 {(,y) 4 A continuous function f(x,y) is guaranteed to have an absolute minimum on the region D, where D = + O True False Question 1 {(,y) 4 A continuous function f(x,y) is guaranteed to have an absolute minimum on the region D, where D = + O True False
Find the absolute maximum and minimum values of the function, if they exist, over the indicated interval. Also indicate the x-value at which each extremum occurs. 200 f(x) = x2 + (0,00) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The absolute maximum value(s) isare) (Simplify your answers. Type integers or decimals rounded to three decimal places as needed. Use a comma to separate answers as needed.) OB. There...
13. The graph of f is shown. State, with reasons, the numbers at which f is not continuous. a) State, with reasons, the numbers at which fis not differentiable. b) 246 0 4 14. Trace the graph of the function and sketch a graph of its derivative directly beneath. a) b) c) 0 any differentiation formulas to find equations of the tangent line and normal line to the curve y at the given point P a) y (2x-3)2 at P-(1,...