Give an example of a continuously differentiable function from to , which has an isolated local maximum at (0,0) and in (-17,9) and (0,3) an isolated local minimum in each case. Justify your answer.
A function having local maxima at (0,0) and local minimum at (-17,9) is
which possesses local maximum value equal to at (0,0) and local minimum value at (-17,9) in the subset
Similarly, for local maximum at (0,0) and local minimum at (0,3) an example is
which attains local maximum value equal to at (0,0) and local minimum value equal to at (0,3) in the subset
Give an example of a continuously differentiable function from to , which has an isolated local...
Consider the function A. Give the intervals of increase and decrease of B. Give the local maximum and minimum values of C. Give the intervals of concavity of f(3) = x +3.03 f We were unable to transcribe this imageWe were unable to transcribe this image
4. True or False. Write true or false in the blanks. a, A continuous function over a closed interval will achieve exactly one local maximum on that interval ______________ b. If f(x) and g(x) both have a local maximum at x=a then has either a local maximum or a local minimum at x=a. ___________ c. If for all x and if a > b, then _____________ d. If is undefined, and if is continuous at x=c, then has a local...
Can you find a differentiable function f(x) defined on the interval [0, 3] such that , and for all x ∈ [0, 3]? Justify your answer (do not write only Yes or No, but explain your answer). We were unable to transcribe this imageWe were unable to transcribe this imagef'(x) <1
Let a continuously differentiable function f: Rn → R and a point x E Rn be given. For d E Rn we define Prove the following statements: (i) If f is convex and gd has a local minimum at t-0 for every d E R", then x is a minimiser of f. (ii) In general, the statement in (i) does not hold without assuming f to be convex. Hint: For) consider the function f: R2-»R given by Let a continuously...
Let be an arbitrary function and A X. i) Show that A ii) Give an example to show that in general A = . iii) Show that, if is injective, then A = iv) Show that, if X and Y are modules; is a homomorphism of modules and A is a submodule of X such that ker, then we also have A = We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe...
8. Constantly Differentiable continuation Determine a function f: R->R that apply to the following properties - For all applies f(x) = sin(x) - For all ,applies f(x) = - f is continuously differentiable r e-oo, 0 OC e1, o0) We were unable to transcribe this image
8. Constantly Differentiable continuation Determine a function f: R->R that apply to the following properties - For all applies f(x) = sin(x) - For all ,applies f(x) = - f is continuously differentiable r e-oo, 0 OC e1, o0) We were unable to transcribe this image r e-oo, 0 OC e1, o0)
Question 6 (1 point) Suppose a function f(x) is differentiable everywhere and has a local minimum at x=c. If f(x)<O when x<c, and f'(x)>0 when x>c, then by the Global Interval Method we know x=c is O a local maximum an absolute maximum a local minimum an absolute minimum
The figure below shows a graph of the derivative of a function . Use this graph to answer parts (a) and (b) (a) On what intervals is increasing or decreasing? (b) For what values of does have a local maximum or minimum? (It asks to be specific). Only the values are needed (not ordered pairs). We were unable to transcribe this imageWe were unable to transcribe this imagepe & Bl apr derivative f' of a function f. Use this graph...
Let Which of the following are TRUE? Select ALL that apply. Please show all your work. a. has a local maximum at whenever is an even integer b. has a saddle point at whenever is an even integer c. has a saddle point at whenever is an odd integer d. has a local minimum at whenever is an odd integer fr, y) = sin(x + 7/2) +y? We were unable to transcribe this imageWe were unable to transcribe this imageWe...