10:[["$","title","0",{"children":"CUET Mathematics - The maximum value of (1/x)^x for x > 0 is | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined To find the maximum value of (1/x)^x for x > 0, rewrite the expression in a simp<=r form: (1/x)^x = 1^x/x^x = 1/x^x = x^-x

Let f(x) = x^-x. To find the maximum, take the natural logarithm: (f(x)) = (x^-x) = -x (x) Let g(x) = -x (x) Since is an increasing function, the maximum of g(x) occurs at the same point as the maximum of f(x).

To find the maximum, take the derivative using the product ru<=: g'(x) = -[(x) + x 1/x] = -[(x) + 1] = -(x) - 1

Setting the derivative equal to zero: -(x) - 1 = 0 (x) = -1 x = e^-1 x = 1/e

Substituting x = 1/e into the original expression: f(1/e) = (11/e)^1/e = e^1/e Therefore, the maximum value is e^1/e."}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$undefined"}],["$","meta","3",{"name":"keywords","content":"CUETMAT,MAT,Calculus,Application of Derivatives"}],["$","meta","4",{"name":"robots","content":"index, follow"}],["$","meta","5",{"name":"category","content":"education"}],["$","meta","6",{"name":"google-site-verification","content":"google"}],["$","meta","7",{"property":"og:title","content":"CUET Mathematics - The maximum value of (1/x)^x for x > 0 is | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined To find the maximum value of (1/x)^x for x > 0, rewrite the expression in a simp<=r form: (1/x)^x = 1^x/x^x = 1/x^x = x^-x

To find the maximum, take the derivative using the product ru<=: g'(x) = -[(x) + x 1/x] = -[(x) + 1] = -(x) - 1

Setting the derivative equal to zero: -(x) - 1 = 0 (x) = -1 x = e^-1 x = 1/e

Substituting x = 1/e into the original expression: f(1/e) = (11/e)^1/e = e^1/e Therefore, the maximum value is e^1/e."}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/past-year-questions/cuet-mathematics/2025/slot-12/12"}],["$","meta","10",{"property":"og:site_name","content":"AfterBoards | CUET Mathematics Preparation"}],["$","meta","11",{"property":"og:image","content":"https://www.afterboards.in/pyp/AfterBoards%20CUET%20Past%20Year%20Papers%20with%20Solutions.webp"}],["$","meta","12",{"property":"og:type","content":"website"}],["$","meta","13",{"name":"twitter:card","content":"summary_large_image"}],["$","meta","14",{"name":"twitter:site","content":"afterboards.in"}],["$","meta","15",{"name":"twitter:title","content":"CUET Mathematics - The maximum value of (1/x)^x for x > 0 is | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined To find the maximum value of (1/x)^x for x > 0, rewrite the expression in a simp<=r form: (1/x)^x = 1^x/x^x = 1/x^x = x^-x

To find the maximum, take the derivative using the product ru<=: g'(x) = -[(x) + x 1/x] = -[(x) + 1] = -(x) - 1

Setting the derivative equal to zero: -(x) - 1 = 0 (x) = -1 x = e^-1 x = 1/e

Substituting x = 1/e into the original expression: f(1/e) = (11/e)^1/e = e^1/e Therefore, the maximum value is e^1/e."}],"$L17","$L18","$L19","$L1a","$L1b","$L1c","$L1d","$L1e","$L1f","$L20"]

CUET Mathematics 2025 22 May Shift 2 PYQs

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