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A: Double integration
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- A differentiable function f has one critical number at x = 2. Identify the relative extrema of f at the critical number when f′(1) = 2 and f′(3) = 6.Consider the function: f(x, y) = 2x3 + xy2 + 5x2 + y2 + 5 Find all the critical point of f. Use the 2nd derivative test to classify the critical points of f. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f has local maximum value(s) at (x,y) = f has local minimum value(s) at (x,y) = f has saddle point(s) at (x,y) =f (x, y) = (2h - y)(y - x^2) a) find the critical points using partial differentiation b) find the single critical point inside the cross-section, A (attached), and show it is local max. using Hessian determinent
- Finding the critical point(s) of f(x) on the given internal. f(x)=(2^x)sin(x) on [-2,6]the continuous function has a critical point. (a)Is the critical point a local maximum or a local minimum? (b)Sketch the graph near the critical point. Label the coordinates of the critical point. 1. f(1) = 5, f ′(1) = 0, f ″(1) = −2 2. h(2) = −5, h′(2) = 0, h″(2) = −4function: f (x, y) = (2h - y)(y - x^2) a) find all critical points of function b) find the one critical point which is within the cross-section, A (or possibly on the boundary of A) *attached*
- Please do help me with this sum, especially the Saddle Point part. Thank you so much Find the critical points, relative extrema, and saddle points of the function. (If an answer does not exist, enter DNE.) f(x, y) = x3 + y3 − 12x2 + 15y2 + 48x + 75y + 62 Relative maximum of f(x, y) = ___________ at (x, y) = (_____________) Relative minimum of f(x, y) = ___________ at (x, y) = (______________) Saddle point of f(x, y) = ____________ at (x, y) = (_______________) List the critical point for which the Second-Partials Test fails. (x, y) = (_______________)f(x)=x^3*ln(x), x>0 a) determine the intervals on which f(x) is concave up and concave down b) based on your answer in part a), determine the inflection points of f(x) as an ordered pair (x,y) c) find the critical numbers of f(x) and use the second derivative test, when possible, to determine the relative extrema.Using the First Derivative Test proved in the videos, prove the following version of the First Derivative Test: If f′ is continuous on the interval [a,b] and if f has exactly one critical point c then f has a maximum at c if f′(a′)>0 and f′(b′)<0 for some a′ and b′ such that a<a′<c<b′<b.