(1 point) Consider the function f(x) = 20x² - 18x2 + 16x - 3. Find F(x)...
6 (1 point) Consider the function f(x) = 1 Let F(2) be the antiderivative of f(x) with F(1) = 0. Then F(3) equals 1111
(1 point) Consider the graph of the function f(x) shown below. (Click on the graph for a larger version) A. Estimate the integral B. If F is an antiderivative of the same function f and F(0) -50, estimate F(7): We were unable to transcribe this image
(1 point) Consider the graph of the function f(x) shown below. (Click on the graph for a larger version) A. Estimate the integral B. If F is an antiderivative of the same function f...
Find the intervals of increase and decrease for the function f(x)= 3 - 16x - 4. Express your answers as inequalities. Separate multiple answers with commas if necessary. If no such answer exists use the DNE button.
(1 point) Consider the function f(t) = 10 sec?(t) – 6t". Let F(t) be the antiderivative of f(t) with F(0) = 0. Find F(t).
(1 point) Consider the function f(x) = 7x – 6 and find the following: a) The average rate of change between the points (-1, f(-1)) and (3, f(3)). o b) The average rate of change between the points (a, f(a)) and (b, f(b)). c) The average rate of change between the points (x, f(x)) and (x + h, f(x + h)).
(1 point) Consider the function f (x, y) = 3x2 + 4y2. f at the point (-4,1) in the direction given by Find the the directional derivative of the angle 0 Find the vector which describes the direction in which f is increasing most rapidly at (-4, 1)
(1 point) Consider the function f (x, y) = 3x2 + 4y2. f at the point (-4,1) in the direction given by Find the the directional derivative of the angle 0 Find...
For the function f(x)=−3−5x^3 find the derivative of the inverse function f-1 at the point x=37. (f−1)'(37)=
(1 point) Consider the function f(x) = on the interval [4,9]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a c in the open interval (4,9) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.
|(a) Consider the following function for > 0 f (x)= = -4x 48x (i) Find the stationary point(s) of this function. (3 marks) (ii) Is this function convex or concave? Explain why. (3 marks) (iii What type of stationary point(s) have you found? Include your reasoning. (4 marks) |(b) Show that ln(a) - a has a global maximum and find the value of a > 0 that maximises it. Do the same for ln(a) - a" where n is a...
(3) Optimization f(x,y) =- 5x² + 4xy - y2 + 16x + 10 8f8f8f (3) Find år 8x8x' 8x8y if 8²5 87 (3b) Find gydydySyox (3d) Classify and determine the relative extrema of the f(x,y).