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Find the two lines that are tangent to y = x2- 2x+1 and pass through the point (5,7).
Call (d) is the equation of the tangent to y = x2- 2x+1, pass through the point (5,7) and have slope k y – y0 = k(x – x0) y – 7 = k(x – 5) y = kx – k5 + 7 we slove system of equations
The two lines that are tangent is: y=8x – 47 y=2x – 17
Find limx→1x-1x2+3-2
3. The circumference C, in centimeters, of a healing wound is approximated by C(r) = 6.28r, where r is the wound’s radius, in centimeters.
Find the rate of change of the circumference with respect to the radius.
Explain the meaning of your answer to part (a) a, The rate of change of the circumference by taking the derivative respesct to the radius by (in centimeters) b, We have C(x)=6.28r is straight line equation, to find the rate of change we suse C’(x), So the rate always change is 6.28
4. When a theater owner charges $5 for admission, there is an average attendance of
180 people. For every $0.10 increase in admission, there is a loss of 1 customer from the average number. What admission should be charged in order to maximize revenue?
Let x be the number of dollars by which the price of $5 should be increased.(If is posgative, the price is decreased). We first express the total revenue R á a function of x. note that the decrease in ticket sale 0.1x when the price loss x dollar R(x)= (Revenue from tickets) = (Number of people).(ticket price) To find x such that R(x) is maximum, we first find R’(x) R’(x)= -20x + 130 This derivative exists for all real number x. thus, the only critical values are where R’(x)=0; so slove that equation: -20x+130=0 -20x=-130
Find the two lines that are tangent to y = x2- 2x+1 and pass through the point (5,7).
Call (d) is the equation of the tangent to y = x2- 2x+1, pass through the point (5,7) and have slope k y – y0 = k(x – x0) y – 7 = k(x – 5) y = kx – k5 + 7 we slove system of equations
The two lines that are tangent is: y=8x – 47 y=2x – 17
Find limx→1x-1x2+3-2
3. The circumference C, in centimeters, of a healing wound is approximated by C(r) = 6.28r, where r is the wound’s radius, in centimeters.
Find the rate of change of the circumference with respect to the radius.
Explain the meaning of your answer to part (a) a, The rate of change of the circumference by taking the derivative respesct to the radius by (in centimeters) b, We have C(x)=6.28r is straight line equation, to find the rate of change we suse C’(x), So the rate always change is 6.28
4. When a theater owner charges $5 for admission, there is an average attendance of
180 people. For every $0.10 increase in admission, there is a loss of 1 customer from the average number. What admission should be charged in order to maximize revenue?
Let x be the number of dollars by which the price of $5 should be increased.(If is posgative, the price is decreased). We first express the total revenue R á a function of x. note that the decrease in ticket sale 0.1x when the price loss x dollar R(x)= (Revenue from tickets) = (Number of people).(ticket price) To find x such that R(x) is maximum, we first find R’(x) R’(x)= -20x + 130 This derivative exists for all real number x. thus, the only critical values are where R’(x)=0; so slove that equation: -20x+130=0 -20x=-130