Former high school math teacher and current software engineer. I spent 10 years teaching middle and high school math from prealgebra through AP Calculus.
Evaluate the difference quotient for the given function. Simplify your answer.
$ f(x) = 4 + 3x - x^2 $ , $ \dfrac{f(3 + h) - f(3)}{h} $
Find the derivative of the function.$ f(x) = \sqrt{5x + 1} $
The graph of $ f $ is shown. Evaluate each integral by interpreting it in terms of areas.
(a) $ \displaystyle \int^2_0 f(x) \, dx $(b) $ \displaystyle \int^5_0 f(x) \, dx $(c) $ \displaystyle \int^7_5 f(x) \, dx $(d) $ \displaystyle \int^9_0 f(x) \, dx $
CAPSTONE Use the fact that the graph of $y=f(x)$ is increasing on the intervals $(-\infty, -1)$ and $(2, \infty)$ and decreasing on the interval $(-1, 2)$ to find the intervals on which the graph is increasing and decreasing. If not possible, state the reason.
(a) $y = f(-x)$(b) $y = -f(x)$(c) $y = \frac{1}{2}f(x)$(d) $y = -f(x-1)$(e) $y = f(x-2) + 1$
Determine which value best approximates the area of the region shown in the graph. (Make your selection on the basis of the sketch of the region and not by performing any calculations.)
(a) -2 (b) 1(c) 4 (d) 6 (e) 9
Evaluate the difference quotient for the given function. Simplify your answer.$f(x)=4+3 x-x^{2}, \quad \frac{f(3+h)-f(3)}{h}$
Winnifred has loans totaling $8,700 when she graduates from college. The interest rate is APR = 5.4%, she will be making monthly payments, and the loan term is 10 years. Calculate the monthly payment:
Write the formula used.Show the values substituted into the formula. Calculate the result. Round your answer to the nearest whole cent.
Calculate the total amount paid over the life of the loan.
What percent of the total amount paid is made up of interest? Round your answer to the nearest whole percent.
Sineoidal Functions
Question: A carnival Ferris wheel with a diameter of 14.0 m rotates once every 16 s. The bottom of the wheel is 2 m above the ground.
a) Sketch the graphs showing one complete cycle.
b) Find the equation of the sine function that gives a rider's height above the ground in meters, as a function of time, in seconds, with the rider starting at the bottom of the wheel.
c) Calculate the height of the person after 11 seconds.
Sketch the graph of a function that satisfies all the given conditions: f'(1) = 0 = f'(-1), f'(x) < 0 if |x| < 1, f'(x) > 0 if 2 > |x| > 1, f'(x) = -1 if |x| > 2, f''(x) < 0 if -2 < x < 0, and inflection point at (0,1).
Consider the following function.f(x) = (x + 4)^2(x - 2)(a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)(b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)increasingdecreasing(c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.)relative maximum (x, y)relative minimum (x, y)
Find the open intervals on which the function is concave up, concave down, or neither. Use a table to show your test values and the sign of f". Write the answers in interval notation. Show all of your work for credit. Write N/A where it is not applicable.Concave up:Concave down:Neither:
