3.1 Homework - Polynomials, Exponential Functions (Homework)

6. [-/1 Points] DETAILS SCALCET9 3.1.034.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Differentiate the function. y = ex+8 + 5 y' Need Help? Read It Master It 7. [-/1 Points] DETAILS SCALCET9 3.1.050. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the first and second derivative of the function. G(r) = Vr + Vr G'(r) = G"(r) = Need Help? Read It Watch It8. [-/1 Points] DETAILS SCALCET9 3.1.057. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P of the gas is inversely proportional to the volume V of the gas. (a) Suppose that the pressure of a sample of air that occupies 0.104 m at 20C is 50 kPa. Write V as a function of P. V ( P ) = (b) Calculate - dv dp - when P = 50 kPa. dv dp What is the meaning of the derivative? O The derivative is the instantaneous rate of pressure with respect to the volume at 20C. O The derivative is the instantaneous rate of change of the temperature with respect to the volume. O The derivative is the instantaneous rate of change of the volume with respect to the temperature. O The derivative is the instantaneous rate of change of the volume with respect to the pressure at 20C. O The derivative is the instantaneous rate of change of the temperature with respect to the pressure at 50 kPa. What are its units? O m3/oc O .C/kPa O . C/m 3 O kpa/m3 O m3/kpa Need Help? Read It9. [-/1 Points] DETAILS SCALCET9 3.1.059.EP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the following function. y = x3 + 3x2 - 9x + 2 Find y'(x). y' ( x ) = The graph of y(x) has a horizontal tangent line when y'(x) is equal to what value? y' ( x ) = 1 Set y'(x) equal to the value above and solve for x. (Enter your answers as a comma-separated list.) X= Find the points on the given curve where the tangent is horizontal. smaller x-value ( x, y ) = larger x-value ( x , y ) = Need Help? Read It10. [-/1 Points] DETAILS SCALCET9 3.1.071. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find a second-degree polynomial P such that P(2) = 11, P'(2) = 11, and P"(2) = 8. P(x) = Need Help? Read It Watch It