Find the difference quotient of f(x) = x² at x = a and simplify. (The difference quotient at x = a is f(a+h)-f(@)).
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- Using the first derivation test, explain why the function f(x)= -2x has no extrema on any open interval.An open box is to be constructed by cutting out square corners of xx-inch sides from a piece of cardboard 9 inches by 8 inches and then folding up the sides. Express the volume of the box as a function of x.Estimate of f′(2):
- Find the domain of the function f(x)=−2x^2−4x+1 Use interval notation to express your answer. Domain:Find the domain of the function. Give result in interval notation f(x) = 8/√8−4xDetermine where the function is concave upward and where it is concave downward. (Enter your answers using interval notation.) f(x) = 3x4 − 30x3 + x − 3 concave upward: ____________ concave downward: ____________
- Identify the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) y = x square root over 100-x2 increasing________ decreasing_________Using the second derivative test, find whether the function: x^3-9x^2-48x+52, has a local minimum or local maximum when x=8Find the intervals where the function is concave up. Use interval notation for your answer. f(x) = 2x3 - 24x - 5
- Identify the open interval on which the function is increasing or decreasing. (Enter your answers using interval notation.) NEED HELPwhat is the domain and range of f in interval notation. write equation for f^-1(x) and domain and range for f^-1(x) in interval notation.Find the absolute extrema of the function on the closed interval. Use a graphing utility to verify your results. f(x) = x3 − 12x, [0, 5]