| 10re", | 2:r3 + 3x² – 12x, r>0 * <0 Given: f(r) = (a) Identify all critical numbers of f. (b) Determine the extreme values of f on [-2, 2]. (Hint: e z 2.71)
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Please answer (a). Thank you
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- 1. Show (in terms of ε - δ) that a function f : R3 → R defined byf(x; y; z) = (2x + 3y + 4z) is uniformly continuous.Suppose f(x,y)=xy(1−8x−10y).f(x,y) has 4 critical points. List them in increasing lexographic order. By that we mean that (x, y) comes before (z, w) if x<z or if x=z and y<w. Also, describe the type of critical point by typing MA if it is a local maximum, MI if it is a local minimim, and S if it is a saddle point.how (in terms of − δ) that a function f : R3 → R defined byf(x, y, z) = (2x + 3y + 4z) is uniformly continuous
- Show that 5 is a critical number of the function g(x) = 2+ (x -5)3but g does not have a local extremevalue at 5.1. Show (in terms of epsilon - delta ) that a function f : [2 ; 7] follows R be defined by f(x) =square root of (x2 + 1) is uniformly continuous.Suppose f(x,y)=xy(1−10x−4y). f(x,y) has 4 critical points. List them in increasing lexographic order. By that we mean that (x, y) comes before (z, w) if x<z or if x=z and y<w. Also, describe the type of critical point by typing MA if it is a local maximum, MI if it is a local minimim, and S if it is a saddle point. First point ( , ) of type Second point ( , ) of type Third point ( , ) of type Fourth point ( , ) of type
- Suppose f(x,y)=xy(1−1x−10y) f(x,y) has 4 critical points. List them in increasing lexographic order. By that we mean that (x, y) comes before (z, w) if x<zx<z or if x=zx=z and y<wy<w. Also, describe the type of critical point by typing MA if it is a local maximum, MI if it is a local minimim, and S if it is a saddle point. First point ( , ) of type ___Second point ( , ) of type ______-Third point ( , ) of type ________-Fourth point ( , ) of type ________Suppose ff is differentiable on (-\infty,\infty)(−∞,∞), f(3)=12f(3)=12, and f'(3)=-2f′(3)=−2. Use linear approximation to estimate f(3.3)f(3.3)construct a suitable Liapunov function of the form ax2 + cy2, where a and c are to be determined. Then show that the critical point at the origin is of the indicated type. 1.dxdt=−x3+xy2,dydt=−2x2y−y3; asymptotically stable