Find the maximum and minimum values, if any, of the following functions given by (i)f(x) = |x+ 2| − 1 (ii)g(x) = − |x+ 1| + 3 (iii)h(x) = sin(2x) + 5 (iv)f(x) = |sin 4x+ 3| (v)h(x) =x+ 1,x(−1, 1)

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(i) f(x) = We know that for every x ∈ R. Therefore, f(x) = for every x ∈ R. The minimum value of f is attained when. ∴Minimum value of f = f(−2) = Hence, function f does not have a maximum value. (ii) g(x) = We know that for every x ∈ R. Therefore, g(x) = for every...
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(i)f(x) = We know thatfor everyx∈R. Therefore,f(x) =for everyx∈R. The minimum value offis attained when. ∴Minimum value off=f(−2) = Hence, functionfdoes not have a maximum value. (ii)g(x) = We know thatfor everyx∈R. Therefore,g(x) =for everyx∈R. The maximum value ofgis attained when. ∴Maximum value ofg=g(−1) = Hence, functiongdoes not have a minimum value. (iii)h(x) = sin2x+ 5 We know that − 1 ≤ sin 2x≤ 1. ⇒ − 1 + 5 ≤ sin 2x+ 5 ≤ 1 + 5 ⇒ 4 ≤ sin 2x+ 5 ≤ 6 Hence, the maximum and minimum values ofhare 6 and 4 respectively. (iv)f(x) = We know that −1 ≤ sin 4x≤ 1. ⇒ 2 ≤ sin 4x+ 3 ≤ 4 ⇒ 2 ≤≤ 4 Hence, the maximum and minimum values offare 4 and 2 respectively. (v)h(x) =x+ 1,x∈ (−1, 1) Here,if a pointx0is closest to −1, then we find for allx0∈(−1, 1). Also, ifx1is closest to 1, thenfor allx1∈(−1, 1). Hence, functionh(x) has neither maximum nor minimum value in(−1, 1). read less
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I am expert in electrical engineering . I have b tech and m tech from nit warangal total experi 10 y

F(-x)= -x+2-1 for maximum. X-2-1 X-2 not equal to f x. F(x)=-x+2-1=-x+1= for minimum.
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Related Questions

For all real values of x, the minimum value of  is

(A) 0 (B) 1

(C) 3 (D)

Let ∴By second derivative test, f is the minimum at x = 1 and the minimum value is given by . The correct answer is D.
Chiranjeevi
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