Partial preview of the text
Download Derivatives overview and more Study notes Pre-Calculus in PDF only on Docsity!
2.2 Defining the Derivative Calculus Find the derivative using limits. If the equation is given as y = given as f(x) 1. f(x) =7— 6x 5éx)= bien 2-66) - (7-60) SR to , use Leibniz Notation: &. . If the equation is =, use Lagrange Notation: f’(x). WRITE SMALL!! 2. y =Sx?2- sy _ Lin SGA} Gath) ~ (G2 -> ‘ii \oo Ax W = Lin Fab -Or- F464 = Lin Babe w2)-» -h- 52 he he, ~ we silty 0h = fim WrHASK Wy _ hioxas-) SO oy = = Ged 1ox+5h-) 7 he S(x)=-6 Ay = (Oy R= x= I 3. y= Voxt2 4. fQ)=5 #2 = = La Berye - ian, Sen se L; as a We W “Sheanya tf5en Sn) Lin == = in SGee ene (5x43) ~ Um (xr ho Wimp 4 (ee) We Ka-DGd Pane a = lie Sx SK4-5x = DREN A XT 30 “eer Ss - ln eS ee eas QASKtD =i 3 (Ses y jb — Uw =) ~ Wee (Km-al(x-3) wv. | Sx) =m For each problem, use the information given to identify the meaning of the two equations in the context of the problem. Write in full sentences! 5. C is the number of championships Sully has won while coaching basketball. t is the number of years since 2002 for the function C(t). C(12) = 3 and C’(12) = 0.4 By 2014, Sully won 3 championships. In 2014, Sully is winning 0.4 championships per year. 6. d is the distance (in miles) from home when you walk to school. h is the number of hours since 7:00 a.m. for the function d(h). d(0.5) = 1.2 and a'(0.5) = —11 At 7:30, | am 1.2 miles from home. At 7:30, | am going back home at 11 miles per hour. 7. W is the number of cartoon shows Mr. Kelly watches every week. x is the number of children Mr. Kelly has for the function W(x). W(7) = 25 and W'(7) =3 8. g is the number of gray hairs on Mr. Brust’s head. x is the number of students in his 4" period. (26) = 501 and g'(15) = 130 If Mr. Kelly has 7 kids, he watches 25 cartoons With 26 kids in his 4th period, Mr. Brust has each week. 501 gray hairs If he has 7 kids, the rate of watching cartoons is With 15 kids in his 4th period, Mr. Brust is increasing by 3 per week. gaining 130 gray hairs per kid. | For each problem, create an equation of the tangent line of f at the given point. Leave in point-slope. 9. f(7) =Sand f'(7) = -2 10. f(—2) = 3 and f’(—2) = 4 11. f(x) = 3x? + 2x; f'@) = 6x+2; x=-2 a ln-4 = 3 ‘(-d)=- =-\o WS =-2(x-#) Y-3= 4(x +2) yen 4-B=-lo(x+) 12. f(x) = 10V6x +1; 13. f(x) = cos 2x; 14. f(x) = tanx; PO =a: x=4 f' (x) = —2sin 2x; x=t f'(x) =sec?x; x= Sty)=lo-9s— = So SC%)= (4) = 0 S(e\-tek = 18 H()= FE = & SCBY= -AsmoR)=- SC8)= ag oe 4 50 = 6(x-4) \)=-alx-%) JAB =4 (x) 2.2 Defining the Derivative Test Prep 4 bes S0) 15. Let f'(x) = lim For what value of x does f(x) = 4? §(2)= 9 eal (A) -4 (B) -1 (C) 1 (E) 4 
