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![Using a Derivative Let f(0) = 3 and 2 < f'(x) < 4
for all x in the interval [-5, 5]. Determine the greatest
and least possible values of f(2).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff1d56c48-5f18-44ea-a8b1-c6aed8363eff%2F2496811e-1059-4f5c-b6c3-c49c91ec0872%2Fmlqnwt6_processed.jpeg&w=3840&q=75)
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- Deduction of the second derivative criterion for optimization of functions <br> of two variables using and as related to TaylorFind the critical point of the function. Then use the second derivative test to classify the nature of this point, if possible. (If an answer does not exist, enter DNE.) f(x, y) = xy + 3 x + 9 y critical point (x, y) = classification Finally, determine the relative extrema of the function. (If an answer does not exist, enter DNE.) relative minimum valuerelative maximum valueTest for homogeneity f(x,y)=tanx-sec2x-cosy
- Find all relative extrema and state the intervals where the function is increasing and decreasing. Show your work using the first derivative test. y= 2+3x-x^3Consider the function on the interval (0, 2π). (a) Find the open intervals on which the function is increasing or decreasing. (b) Apply the First Derivative Test to identifyall relative extrema. (c) Use a graphing utility to confirm your results.Using the Second Derivatives Test, your task is to find all relative extrema and saddle points of the given functions. Show Complete Solutions
- Zero directional derivative In what directions is the derivative of ƒ(x, y) = (x2 - y2) / (x2 + y2) at P(1, 1) equal to zero?Compute the derivative of f(x) = e^x/ x^n for constant n using the specified methods: (a) The quotient rule (b) The product rule. Please type it outShow full solution: Find all relative extrema and saddle points of the following function using Second Derivatives Test f(x,y) = exy + 2
- find the critical numbers of (if any), (b)find the open interval(s) on which the function is increasing ordecreasing, (c) apply the First Derivative Test to identify allrelative extremaFind the critical points of the function. Then use the Second Derivative Test to determine whether they are local minima, local maxima, or saddle points (or state that the test fails). f (x, y) = x ln(x + y)Consider the function on the interval (0, 2pi). (A) find the open intervals on which the function is increasing or decreasing (B) apply the First Derivative Test to identify all relative extrema