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Derivatives

Differentiation for a Tangent Line

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.

Derivatives, Differentiable Functions and Rate of Change

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

Finding Derivatives and Logarithmic Differentiation

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).

Sunrise Baking Company markets dough nuts through a chain of food stores.

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

Implicit Differentiation

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)

Mathematics: Derivatives and Rates of Change

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

Maximum Values by Partial Differentiation

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

Chain rule?

Please explain chain rule i'm a visual person please show several examples

Quotient and Composite Rules

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]

How fast is the brick falling after 2 seconds have passed?

A brick comes loose from near the top of a building and falls such that its distance s (in feet) from the street (after t seconds) is given by the equation s(t) = 200 - 16t^2 (see equation in attached file) How fast is the brick falling after 2 seconds have passed?