(a) The graph in the figure given below is made of line segments joined end to end. At which points of the interval [-2,6] is f' not defined? Give reasons for your answer. (b) Graph the derivative of f. -B (-2,0) -4 4- 2 (0.2) 2 6 (6,2) (1,-1) (4, -1) X "?
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- The folowing is a reworded question from very last night . A printed solution of a length of curve function, f(y) = x3 - 1/4x3, I was studying was solved to a point by finding the derivative of the function, square the result, and then it followed its own instruction "simplify the integrand" and gave [ 1 + (x6 - 1/2 + 1/16x6) dx ]1/2 . It was very early in the morning and I did not recognize the source for the middle term (- 1/2) which had some unstated algebraic process. Would you please give me a step-wise understanding of this algebraic process? I do not need the rest of the solution nor its answer.a. Find the function f given that the slope of the tangent line to the graph of f at any point (x,f(x)) is xe-2x and that the graph passes through the point (0,3). b. In keeping with the projected increase in worldwide demand for steam coal, the boilerfiring fuel used for generating electricity, the management of Consolidated Mining has decided to step up its mining operations. Plans call for increasing the yearly production of steam coal over its current level by: 2te-0.05t million metric tons/year for the next 20 years. The current yearly production is 20 million metric tons. Find a function that describes Consolidated’s total production of steam coal at the end of t years. How much coal will Consolidated have produced over the next 20 years if this plan is carried out?True or False The graph of y = cos x is decreasing on the interval (0, π).
- Find the differential eqn. of the ff. family of curves: a.) Straight lines with slope half the value of the x-intercept b.) Circles with center on the y-axis c.) Circles with center on the line y = x, and passing through the originConsider the function f(x) = 4x – x2 and the point P(2, 4) on the graph of f. Part A) Graph f and the secant lines passing through P(2, 4) and Q(x, f(x)) for x-values of 3, 2.5, 1.5. part B) Find the slope of each secant line. Part C) Use the results of part (b) to estimate the slope of the tangent line to the graph of f at P(2, 4).Describe how to improve your approximation of the slope.5)Let f ( x ) =3x4 + 4x3 Find the derivative. b)Find the critical numbers.
- A, B and c are arbitrary constants. Primes denote derivatives with respect to x. If (image attached) =, then y' =1) Describe the purpose of finding the first and second derivatives to sketch a graph of functions. 2) Find all relative extrema using the second derivative test.a. f(x) = x^2(6 − x)^3b. g(x) = x^3 −5x^2 +7xA cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 16cm by 30cm by cutting equal squares from the four corners and turning up the sides. What is the domain of V? Find the derivative of V(x) with respect to x.
- 5. Why does it make graphical sense that the derivative of aconstant is zero? That the derivative of the identity function is constantly equal to 1? That the derivative of a linearfunction f(x) = mx + b is equal to m?The function f is defined by f(x)=x/(x+2). What points (x, y) on the graph of f have the property that the line tangent to f at (x, y) has slope 1/2?My topic is about Higher Order Derivatives and Optimization for reference. A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 10 in by 17 in by cutting equal squares from the four corners and turning up the sides. Find the length of the side of the cut-off square so that the box has the largest possible volume.