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- In a certain company, the income from the sale of x thousand pieces of products is given by I (x) = 9x, while the cost of making the same x products is given by C (x) = x ^ 3-6x ^ 2 + 15x + 1. Assuming that I and C are in thousands of dollars and everything produced is sold, what is the maximum profit the producer can make? Argues using first or second derivative criteria.Find the partial derivative of the following y = 3x2z + xz3 – 3z/x2FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORM ( 1. y = Arctan√3x−4/4 2. y = 2 Arccos ( 1 -x/2) + √4x − x2 3. y = ln (x3(x−1)/(x−2)^2) 4. y =e^3x−e^−3x/e^3x+e^−3x 5. x =t/t−1, y =t2/t2−1
- suppose xy3-80=3xy-z compute dz/dx at the point (-3,-2,2)find the first and second derivatives. 1. y = -x2 + 3 2. y = x2 + x + 8 3. s = 5t3 - 3t5 4. w = 3z7 - 7z3 + 21z2 5. y = 4x3/3 - x + 2ex 6. y = x3/3 + x2/2 +e-x 7. w = 3z-2 - 1/z. 8. s = -2t-1 + 4/t2 9. y = 6x2 - 10x - 5x^(-2) 10. y = 4 - 2x - x-3 11.r= 1/3s2 - 5/2s 12. r = 12/u -4/u3+1/u4Solve the initial-value problem for yy as a function of xx. (64−x2)dydx=1,y(0)=5(64-x2)dydx=1,y(0)=5
- Find the linearization of ƒ(x) = 2x at x = 0. Then round its coefficients to two decimal places.Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnYJesaki Inc will sell N units of product after spending $x thousand in advertising, as given by N= 66 x−x2. Use differential approximations to estimate the increase in sales that will result by increasing the advertising budget from $10,000 to $10,589. Round to the nearest integer. $
- What is the derivative of k(y)=(6y^−1+3y^−2)(6y^−3+4y^−4)?Suppose f is differential equation on (-inf, +inf), f(3)=12 and f'(3)=-2 use linear approximation to estimate f(3.3)."Ex+y=∫-1.51.5x fx dx+∫-1.51.5y fy dy=∫-1.51.5x11.5--1.5dx+∫-1.51.5y11.5--1.5dy=∫-1.51.5x13dx+∫-1.51.5y13dy=13∫-1.50-xdx+∫01.5xdx+∫-1.50-ydy+∫01.5ydy=13-x22-1.50+x2201.5+-y22-1.50+y2201.5=13-(02--1.52)2+1.52-022+-(02--1.522+1.52-022=131.125+1.125+1.125+1.125=4.53=1.5" Could you write this part for a better understanding? Thank you.