Please help me solve these questions and I have attached the answers sheet also

ANSWERS: 1. a. 2 b. O c. -2 d. 0 2. a. Approximates the slope of the tangent line at x = a, using the slope of the secant line at x = a and x = a + h. b. Approximates the slope of the tangent line at x = a, using the slope of the secant line at x = a + h and x = a h. This is how Nderiv works. c. Slope of the tangent line at x = a. 3. 3. Sometimes b. Must be true 4. Corner Points, Vertical Tangent Lines, and Discontinuities 5. f'(x) = 4X 8 You should have used the definition. 6. a. f'(x)=3X25x+'l, f"(x)=6x75 b. X: 0.2324,1.434 c. x= 7. a. f'(x) =10x4 + 7 sin(x) b. 32: = 6xtan(x) + 3x2 sec2(x) 3 2 c. (x) = (x 7)sec(x)t3an(x23x sec(x) d. \"(X) = 4csc2(4x) (x 7) e. f'(x) = 6(3)(5 + 8)515x4 f. g(x) = 6xcos(6x3) 3x2[18x2 sin(6x3)] g. h'(x) = 4sin3(2x5)cos(2x5)10x4 h. g = et3(3t3 + 1) -15x-6 6 8 X Y -2 + 2x i. f' (x ) = 5 3 j. y' = 5x' + 13x - 30x-2 (5x2 + 1) 2 k. 8 2x3 2x (5x2 +9) 1. dy _20 23 _ 15 x -1/2 + 8 5 x 2 + 3 (5 x2 + 3) 2 dx 3 2 ( x3 + 1 ) - (2) ( 2x + 3 ) 1/2 + ( 2x + 3) 123x -5x3 - 9x2 + 1 m. f' ( x ) = ( x 3 + 1 ) 2 (2x + 3) /2 ( x3 + 1) 2 n. 3 dy =3 sin 3(3x2) cos(3x2)6x dx 8. a. .4 b. 0.6637 9. y = 3x - 2 dy 4 dy _ 192y - 48 y 10. a . dy -1-7y C . dx b. 7x dx tan(y) sec (y) dx 56y' - 24y (6x + 7y) 11. 2.195 in./sec. 12. - ft/min 9TT 13. 19.2 knots/hr 14. -0.3 m/secQUESTIONS: 1. Given the graph of g(x), estimate a- g'( 4) 2. Explain what each of the formulas mean f(a + h) f(a) f(a + h) f(a h) . Iim f(a + h) f(a) h 2h [7 A O h 3. Determine whether the following statements MUST be true or are at least SOMETIMES false. Justify your answers. a. If f is continuous at a point x, then it is differentiable at x. b. If f is differentiable at a point x, then it is continuous at x. 4. List the ways a function is not differentiable. 5. Let f(x) = 2x2 8x + 1, compute f'(x) by using the definition. Show your work. 6. Let f(x) = x3 2.5)(2 + x + 8 Find f'(x), and f\"(x). Find the relative extremes of f(x). Find the inflection points of f(x). Make an accurate graph of f(x). PE'P'P' 7. Find the derivatives. a. f(x) = 2x5 - 7 cos(x) b. y = 3x tan(x) c. g(x) = sec (x) x3 - 7 d. h(x) = cot(4x) e. f(x) = (3x5 +8)6 f. g(x) = 3x2 cos(6x3) g. h(x) = sin*(2x5) h. S= te i. y = 3 2 8 + + 5x3 + X2+5 J. f ( x) = x - 2x+ 3 3x 5x2 +1 k. g(X) = 2x3 1. y = 48x5 + 3 5x2 + 3 + 8x + 5 Vx5 m. f(x) = V2x + 3 x3 +1 n. y = /sin' (3x2)