Question

3.1.37 a. Find the derivative function f' for the function f. b. Find an equation of the line tangent to the graph off at (a f(a) for the given value of a. c. Graph fand the tangent line. f(x) = 2x²+x-1, a=-1 a.f'(x)=

Answer 1

Given Fen) = 2012/04 Both side derivative with respect to a d for - Flow - d (222 +224) dx dx Fl(a)=4041 Henu Derivative of fu) = 44+1 (Ang) (b) Equatton of tangent line at (9HQ) and opo slope flow - 42+1 at a=-1 Now a=-1 then F(-1) = 2(-1)²+(1)-1 F(-1) = 2-1-1= Hence point (-1,0) and slope at = -1 then [flow] =-4+1 = -3 at a=-1 Hence tangent line Equation at point (410) then 19-0) = -3/4+1) y = -3 2-3 y +30=-3 Ans

Hoo - 1 ) ce Graph f and tangent line function Fox) = 2x2+x-1 et y = f(x) = 24 2+2-1 at a=0 then y=-1 Henu point (0-1) = A Hence point (1,2)=B then y=0 Hence point (-1,0)=C N=1 then y = 2 1=-| and tangent line y=-32-3 at 1=0 then y=-3 Hence point (0-3) y=0 then -32= 13 Hence point (110) a=7 HAL=24 ²+2-1 (112) (0-3) tangent line y=-34-3