Suppose that f: [a,b]  R is differentiable, that 0 < m f '(x) M for x є [a,b], and that f(a) < 0 < f(b). Show that the equation f(x) = 0 has a unique root in [a,b]. Show also that for any given x1 є [a,b], the sequence (xn), xn+1 = xn - for n = 1, 2,..., is well defined (i.e. for each n, xn є [a
See attached file for full problem description. 1) Find the partial derivatives with respect to x, y, and z of the following functions: (a) f(x, y, z) = ax2 + bxy + cy2, (b) g(x, y, z) = sin(axyz2), (c) h(x, y, z) = aexy/z^2, where a, b, and c are constants. 2) Find the partial derivatives with respect to x, y, and z of t
Differentiation 1. Show that if the tangent to y=ekx at (a, eka) passes through the origin then a=1/k. 2. Find the value of a and b so that the line 2x +3y = a is tangent to the graph of f(x)=bx2 at the point where x = 3. See attached file for full problem description.
1. Functions f, g, and h are continuous and differentiable for all real numbers, and some of their values and values of their derivatives are given by the below table. x f (x) g(x) h(x) f'(x) g'(x) h'(x) 0 1 -1 -1 4 1 -3 1 0 3 0 2 3 6 2 3 2
2. Find d y / d x : a) x^2 + xy − y^3 = x y ^2 b) sin ^ 2 y = y + 2 c) y = sqrt((x^2+1)/(x^2 - 5)) d) y = x^(ln sqrt(x)) 3. If x ^y = y ^x , use logarithmic differentiation to compute dy / dx at the point (3, 3).
See attached file for full problem description. Find the derivative
Sunrise Baking Company markets dough nuts through a chain of food stores. It has been experiencing overproduction and underproduction because of forecasting errors. The following data are its production in dozens of doughnuts for the past four weeks. Doughnuts are made for the following day; for example, Sunday's doughnut pro
Find an equation of the line tangent to the curve. See attached file for full problem description. Using implicit differentiation to find an equaiton of the line tangent to the curve x^3 + 2xy + y^3 = 13 at the point (1, 2)
"Define f(x) to be the distance from x to the nearest integer. What are the critical points of f."
Find any relative extrema of the fx f(x) = arcsin x - 2x
Find derivative h(x) = x^2 arctan x
Find the derivative of the f(x) f(t) = arcsin t^2
G(x)= ln(cosh x)
Y=cosh^2 (x^3)
Y=cosh(e^(x^2))
Y= ln(3+7x)
Y= x/(e^x +1)
After t years, the value of a car purchased for V(t) = 20,000(3/4)^t (a) use a graphing utility to graph the function and determine the value of the car 2 years after it was purchased. (b) Find the rates of change of V with respect to t when t = 1 and t - 4. (c) free hand stetch graph of V'(t) and determine the horizont
Please see the attached file for the fully formatted problems.
Please find the derivative of the function. y= 6^(-2x)
Need some help finding the max value of a multi-variable function as follows exp ^2x - 2x-2y^2+y and the second one is -(2-x)^2y^2-y I am confused as to how to take the partials with the exponential in the first problem and with the - sign outside the parenthesis in the second problem. If you can work out the
Please explain chain rule i'm a visual person please show several examples
Y = ln[(1+ e^x)/(1-e^x)] keywords: natural log
Find the derivative g(t) = e^-3/t^2
Find the derivative : y = x^2e^-x
Find the derivative: y = e^-x^2
Let f′ (x) = √x and f(9) = 19. Find f(x) __ Let f′ (x) = √x and f(9) = 19. Find f(x)
Find the derivative of f(x) = 3 ln x
1. a. use quotient rule to find derivative of this function. f(x) = (20+16x-x^2)/(4+x^2). b. Find any stationary points of the function from 1a. An use the first derivative test to see whether they are local maximum or local minimum of f(x). c. what are the maximum and minimum values of the function f(x) at interval [-6,2]
Two problems are included in attachment.