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The cost function C(x) and the selling price of each article, p(x) are given below. Determine the profit function P(x).
Find the piecewise formula of the graph below.
For the function , what is the largest interval on which is increasing?
A telecommunications company needs to install a fiber optic cable from a central office to a new development miles away on the opposite side of a lake. The lake is ft wide. The cost of laying the cable under the lake is \( per foot and \) per foot along the road. Determine the least expensive point for the cable to reach the development if it is less than or greater than ft from the starting point along the road.
Apply the transformations on the graph of p(x)=x into the graph of h(x)=4x−3−6 . Check your work with the help of a graphing calculator.
Simplify the composite function a(b(c(x))) given the following:
a(x)=−x3
b(x)=cos(x)
c(x)=x
Write the logarithm log5120 in terms of the natural logarithm. Evaluate the value of the new logarithm with the help of a calculator. Write your answer using four decimal places.
Use a graphing calculator to decide if these functions differ by a constant.
and
Given that loga(p)=0.42 and loga(r)=0.91 find the value of loga4rp.
For the given function, find the inverse.
f(x)=−5x+3
A runner's position along a track is recorded at various times during a race. The data is presented in a table. Find the runner's average velocity between the time interval of 0 to 2 seconds.
Find the value of given that .
A coffee shop charges for Wi-Fi access based on the time used. The graph of the charge function for is given below. Write the intervals of continuity of .
The cost function C(x) and the selling price of each article, p(x) are given below. Determine the profit function P(x).
C(x)=−0.03x2+70x+75
p(x)=80−0.02x
Determine the derivative of the function using the definition:
Given a function that models the height (in centimeters) of a plant days after it was planted, estimate from the provided graph. What does this derivative indicate?
Determine whether the following piecewise function is differentiable at .
The graphs of and are shown. Find if .
Calculate the fourth derivative of the function .
Determine the derivative of .
Given that , , , and , find the derivative of at .