Question

Need answer all question and draw

Below is the graph of y= f'(x). Use the graph to answer the questions that follow. -4 -3 1. On what intervals is f(x) decreasing? Write your answer in interval notation. 2. What is the total change in f as x goes from 1 to 2? 3. At what value(s) of x does take on a local maximum? If there are none, write "NONE" in the answer space. 4. If f(-2)=-3, what is the value of f(l)? 5. If f(-2)=-3, sketch the graph of y = f(x). On your graph, label all extrema with their coordinates. If approximations are necessary, write numbers in decimal form rounded to the nearest tenth.

Answer 1

from figure 8(n) = 2x+4 , pra't42) 2 ) ical Hence [-5-1] 1-2 +1} (-1).] =994, (1; 2) 5] Hence f(a)= x²4424C in [5,-1] Now, ff2) = -3 flom) x?tunt in [-5,-1] -()=f(1) = -2 Now, fm2 = -2h state Now, f(-x) = -2 =) ( =- - fem) -- +9-4 in E-1, ]' tei) = 0 Now, flm) = 284ntle f(1) =0 » G22 i flomla 22 2x3 4n+2 in [1, 2) f(2)= 2 cilj) pen) --22422273, f(2)=2 =) (3? fa-221-6, s] fen) = 2 tunti Le leth-s [-1 0 = 222_untz , [, 2) --+22,125] 2 Now) to vi [-5, -1) ) 2

1 fm) is decreasing in ES, 2] and [us] 2) Total change of f as a goes from 1 to aj fe)-81) = 2-0-2 3) 'f' lakes locade maximum nalue af n = 4 and the maximum in 7.33 The value of fl.)- o Sketch of f(x) 10 Locul Maximum (4,7.33) (2, 2) Not x2 + 4x + 1 4 5 (1,0) (-2,-3) tu + 2x2 10 3 Local Minimum 2x2 - 4x -10