Analyzing critical points Find the critical points of the following functions. Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum , local minimum , or saddle point. Confirm your results using a graphing utility. 25. f ( x , y ) = x 2 + y 2 − 4 x + 5
Analyzing critical points Find the critical points of the following functions. Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum , local minimum , or saddle point. Confirm your results using a graphing utility. 25. f ( x , y ) = x 2 + y 2 − 4 x + 5
Solution Summary: The author explains how to find the critical points for the function f(x,y)=sqrtx2+y
Analyzing critical pointsFind the critical points of the following functions. Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, local minimum, or saddle point. Confirm your results using a graphing utility.
25.
f
(
x
,
y
)
=
x
2
+
y
2
−
4
x
+
5
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
Use the properties of logarithms, given that In(2) = 0.6931 and In(3) = 1.0986, to approximate the logarithm. Use a calculator to confirm your approximations. (Round your answers to four decimal places.)
(a) In(0.75)
(b) In(24)
(c) In(18)
1
(d) In
≈
2
72
Find the indefinite integral. (Remember the constant of integration.)
√tan(8x)
tan(8x) sec²(8x) dx
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