To findthe minimum or maximum of a function that is not constrained, that is, there are no restrictions on range of thefunction, you take thederivative of thefunction, set it equal to zero, and solve for the variable. The intuition is that thederivative is the instantaneous slope of thefunction. A minimum or maximum occu
1. Compute thederivative of the given function and findthe slope of the line that is tangent to its graph for the specified value of the independent variable. (Compute thederivative of thefunction from the definition only, using limits. More advanced methods are not allowed here. Show your work.)
(i) f(x) = x^2 - 1
x = -
This question concerns thefunction f(x)=x^3 +3x^2 −24x+40.
(a) Findthe stationary points of this function.
(b) (i) Using the strategy to apply the First Derivative Test, classify the left-hand stationary point found in part (a).
(ii) Using the Second Derivative Test, classify the right-hand stationary point found in part
Given y = f(x) = x2 + 2x +3
a) Use the definitional formula given below to findthederivative of thefunction.
b) Findthe value of thederivative at x = 3.
Given, y = f(x) = 2 x3 - 3x2 + 4x +5
a) Use the Power function to findderivative of thefunction.
b) Findthe value of thederivative at x =
A. Write a function for your profits for each price you charge. This is done by multiplying (P-.5) times your function (y= -100x + 250). I.e. if your function is Cups Sold = 1000 - 100P, your profit function would be (P - .5)*(1000 - 100P).
B. Calculate the first derivative of your profit function, and create another table
Let f(x) = x2 + 4x.
(a) Findthederivative f 'of f.
(b) Findthe point on the graph of f where the tangent line to the curve is horizontal.
Hint: Findthe value of x for which f '(x) = 0.
(c) Sketch the graph of f and the tangent line to the curve at the point found in part (b).
Findthe slope m of the tangent line to