1.The area Aof a disk of radius r is given by the formulaA= r². Assume that the area increases at a rate of 4ft²/sec. Find the rate with which the radius increases at the moment when the diameter d=18ft. (Enter your answer correct to at least five decimal places, you may use the value ofprovided by your calculator, or alternatively use 3.1415926535 )

2.Given f(x)=(x-1)³(x-2)² do: (a)find f'(x) and(b) evaluate f'(3). Enter your integer answer for part (b) in the box (using digits, and a negative sign, if necessary, like 35 or -41 ).

3 As a snowball melts,its area Adecreases at the rate 2cm²/minute.Find the rate with which it radius decreases, when the radius r=3cm.Use that the surface area of a sphere is given by the formula A=4r² (where isapproximately3.1415926535). Enter your answer as a number only, correct to at least four decimal places, no sign.

4. For the function f(x)=x³+3x²-45x+5find the positive critical number. Enter your answer as an exact integer.

5. Givenf(3)=-3,f(68)=-5, f'(3)=4, f'(68)=10, g(68)=3, and g'(68)=7, evaluate (f(g(x)))' when x=68.Enter your answer in the box as an integer like -30or 43

6. If f(x) = (4x^-1+2x² )³,find f'(x)and evaluate f'(1).In the box enter your answer forf'(1) as an integer,like -35or 356

7.Find the second derivativeof f(x)=3x ln(x) and evaluate it at x=3.(Enter your answer correctto at least three decimal places.)

8 A particle moves along a straightline according to the law of motions(t)= 1/6t^3 -5t^2+6t- 2. Find the velocity at the moment t=4. (Enter your answer as an integer, using digits, not words. Like 78 or -5, not seventyeight or negative five.)

9.Given f(x)=find the derivative f'(x).

10.Given 3x²y -y³= 5x - 7 , useimplicit differentiation to find the derivative y'=dy/dxand evaluateitat the point (x,y)=(1,2).

11. A particle moves along a straightline according to the law of motions(t)=1/6t^3-5t^2+9t-2. Find the acceleration at the moment t=4. (Enter your answer as an integer, using digits, not words. Like 78 or -5, not seventyeight or negative five.)

12 Given f(x)=cos(x^6-2x+1) find the derivative f'(x).

13Find the equationof the tangent line to the graph off(x)=sin(x^4-2x+1 when x=1.