Mathematics 1

Yanıt Açıklaması:

Yanıt Açıklaması:

Yanıt Açıklaması: The derivative of the function f(x) = 2x 3 + 3x 2 + 5x is equal to 6x 2 + 6x + 5. f'(2) = 6*(2) 2 + 6*2 + 5 = 24+12+5=41 and f(1) = 2*(1) 3 + 3*(1) 2 + 5*1 = 2+3+5=10. the sum of these two values 41+10= 51. The answer is C.

Yanıt Açıklaması: So, the slope of the tangent line to the graph is zero at (-3/2, -37/4). The answer is B.

Yanıt Açıklaması: (x 2 – 1) / (x 2 - 1) (x 2 + 1) = 1 / (x 2 + 1) ; 1 / (1 + 1) = 0.5 ; x ≠ 1 . pg. 108 . Correct answer is A.

Yanıt Açıklaması: The equation of tangent line is given by the formula: y – f(x 0 ) = f'(x 0 )(x – x 0 ) x 0 =2 and f(x 0 )=1 are given. Since f(x)=x 2 -2x+1 then f'(x)=2x-2 and f'(x 0 )=2*2-2=2 for x 0 =2. Thus the equation for the tangent line will be: y-1=2(x-2) y-1=2x-4 y=2x-3

Yanıt Açıklaması: (x – 2) (x + 1) / (x – 2) = x + 1 ; x ≠ 2 . pg. 108. Correct answer is E.

Yanıt Açıklaması: A function is increasing where its first derivative is positive. Thus, we have to find the intervals where the first derivative of function is positive. f(x)=x 3 -12x f'(x)=3x 2 -12 So the function is increasing where f'(x)>0 Namely: 3x 2 -12>0 3x 2 >12 x 2 >4 This is possible when x>2 and when x<-2 Thus the function is increasing in the interval (-∞, -2)U(2,∞)

Yanıt Açıklaması: We know that the total revenue function is given by R=p*x, Therefore, the answer is E.

Yanıt Açıklaması: (x 2 + x k x + k 2 x 2 ) / (x + x k x + k x) = (x 2 (1 + k + k 2 )) / (x (k x + 1 + k)) = (x (1 + k + k 2 )) / (k x + 1 + k) = 0. pg. 182. Correct answer is B

Yanıt Açıklaması: The break-even point is the point at which cost or expenses and revenue are equal: there is no net loss or gain, and one is said to have “broken even.”

Yanıt Açıklaması: f(x)=x²-4x+12 f'(x)=2x-4 f'(x)=2x-4=0 ›x=2 f''(x)=2, 2>0 local minimum. f(2)=4-8+12=8

Yanıt Açıklaması: at (1, -2, -1) : ?F / ?x = z = -1 ; ?F / ?y = -y = 2 ; ?F / ?z = x – y = 3 ; -1 (x – 1) + 2 (y - (-2)) + 3 (z - (-1)) = -(x – 1) + 2 (y + 2) + 3 (z + 1) = -x + 1 + 2 y + 4 + 3 z + 3 = -x + 2 y + 3 z + 8 = 0 . pg. 187. Correct answer is A.

Yanıt Açıklaması: Break-even point is the point where the total cost and the total revenue are equal C(x)=R(x). For our question, R(x)=p*x=3x and C(x)=v*x+a=1,5x+2750. 1,5x+2750=3x,   1,5x=2750,   x=1833,33. The answer is B.

Yanıt Açıklaması: The first derivative must be equal to zero and the second derivative must be positive for a minimum value of a function. Thus: f(x)=x 2 -6x+5 f'(x)=2x-6=0 so 2x=6, x=3 and when x=3 y=f(x)=9-18+5=-4 The second derivative is: f''(x)=2>0 Thus for given function, point (3,-4) is the minimum.

Yanıt Açıklaması: Since the profit is revenue minus the cost we have P(x)=360x-(4800+120x)=240x-4800. Now, to find whether the company loses or makes money insert x=30 into the profit function: P(30)=240·30-4800=+2400, which means that the company gains 2400 TL.

Yanıt Açıklaması: we need to factorise the ratio which follows as ; f(x)=(x²-1)/(x-1)=(x-1)(x+1)/(x-1)=x+1 and if we put "1" instead of x, then the answer will be 1+1=2.

Yanıt Açıklaması: by fractionating the function f(x)=(x-2)(x+2)/(x-2)=x+2 then lim x›2 x+2= 4